PUBLICATIONS

- "Peculiarities of a Free Massless Spin-3/2 Field Theory"
- C. M. Bender and B. M. McCoy
- Physical Review
**148**, 1375 (1966)- "Free Massless Fields as Infinite-Dimensional Representations of the Lorentz Group"
- C. M. Bender
- Physical Review
**168**, 1809 (1968)- "Analytic Structure of Energy Levels in a Field-Theory Model"
- C. M. Bender and T. T. Wu
- Physical Review Letters
**21**, 406 (1968)- "Anharmonic Oscillator"
- C. M. Bender and T. T. Wu
- Physical Review
**184**, 1231 (1969)- "Generalized Anharmonic Oscillator"
- C. M. Bender
- Journal of Mathematical Physics
**11**, 796 (1969)- "Does Renormalized Perturbation Theory Diverge?"
- C. M. Bender, J. E. Mandula, and B. M. McCoy
- Physical Review Letters
**24**, 681 (1970)- "Covariant Energy Density in Free Massless Field Theory"
- C. M. Bender and D. J. Griffiths
- Physical Review D
**1**, 2335 (1970)- "Lorentz Transformation Laws of Interacting Radiation-Gauge Fields"
- C. M. Bender and D. J. Griffiths
- Physical Review D
**2**, 317 (1970)- "Large-Order Behavior of Perturbation Theory"
- C. M. Bender and T. T. Wu
- Physical Review Letters
**27**, 461 (1971)- "One-Dimensional Field Theory"
- C. M. Bender
- Invited talk in
*Particles and Fields-1971*(Proceedings of the Rochester- Meeting of APS/DPF, August 30 to September 2, 1971),
- Ed. by A. C. Melissinos and P. F. Slattery
- (American Institute of Physics, New York, 1971)
- "Covariant Derivatives of Infinite-Dimensional Fields"
- C. M. Bender and D. J. Griffiths
- Journal of Mathematical Physics
**12**, 2151 (1971)- "Path-Integral Approach to the Magnetic-Impurity Problem. I."
- D. J. Amit and C. M. Bender
- Physical Review B
**4**, 3115 (1971)- "Anharmonic Oscillator with Polynomial Self-Interaction"
- T. I. Banks and C. M. Bender
- Journal of Mathematical Physics
**13**, 1320 (1972)- "Anharmonic Oscillator. II. A Study of Perturbation Theory in Large Order"
- C. M. Bender and T. T. Wu
- Physical Review D
**7**, 1620 (1973)- Reprinted in: J. C. Le Guillou and J. Zinn-Justin (eds.),
*Large-order behaviour of perturbation theory*(North-Holland, 1990), p. 41-57- "Coupled Anharmonic Oscillator. I. Equal Mass Case"
- T. I. Banks, C. M. Bender, and T. T. Wu
- Physical Review D
**8**, 3346 (1973)- "Coupled Anharmonic Oscillators. II.Unequal Mass Case"
- T. I. Banks and C. M. Bender
- Physical Review D
**8**, 3366 (1973)- "Permanently Bound Quarks - New Solutions to Old Field Equations"
- C. M. Bender, G. S. Guralnik, and J. E. Mandula
- Physical Review Letters
**32**, 1467 (1974)- "Numerical Study of Energy-Level Crossing"
- C. M. Bender, H. J. Happ, and B. Svetitsky
- Physical Review D
**9**, 2324 (1974)- "Asymptotic Freedom and the Lee Model"
- C. M. Bender and C. Nash
- Physical Review D
**10**, 1753 (1974)- "Theories of permanently Bound Quarks"
- C. M. Bender, G. S. Guralnik, and J. E. Mandula
- Physical Review D
**11**, 409 (1975)- "Self-Consistent Binding Force Between Quarks in One Dimension"
- C. M. Bender, G. S. Guralnik, and J. E. Mandula
- Physical Review D
**11**, 429 (1975)- "Meson Decay in a Theory of Bound Quarks"
- C. M. Bender, G. S. Guralnik, and J. E. Mandula
- Physical Review D
**11**, 438 (1975)- "Statistical Analysis of Feynman Diagrams"
- C. M. Bender and T. T. Wu
- Physical Review Letters
**37**, 117 (1976)- "Zero-Point Energy of Fields in a Finite Volume"
- C. M. Bender and P. Hays
- Physical Review D
**14**, 2622 (1976)- "Numerical Study of Truncated Green's Function Equations"
- C. M. Bender, G. S. Guralnik, R. W. Keener, and K. Olaussen
- Physical Review D
**14**, 2590 (1976)- "New Approach to the Calculation of
*F*in Massless Quantum Electrodynamics"_{1}(α)- C. M. Bender and R. W. Keener
- Physical Review D
**15**, 1572 (1977)- "New Approach to the Calculation of
- "Numerological Analysis of the WKB Approximation in Large Order"
- C. M. Bender, K. Olaussen, and P. S. Wang
- Physical Review D
**16**, 1740 (1977)- "Path-Integral Formulation of Mean-Field Perturbation Theory"
- C. M. Bender, F. Cooper, and G. S. Guralnik
- Annals of Physics
**109**, 165 (1977)- "Perturbation Theory in Large Order"
- C. M. Bender
- Invited talk given at the Second Los Alamos Workshop on Mathematics
- in the Natural Sciences (August, 1976)
- Advances in Mathematics
**30**, 250 (1978)- "Gauge-Fixing Degeneracies and Confinement in Non-Abelian Gauge Theories"
- C. M. Bender, T. Eguchi, and H. Pagels
- Physical Review D
**17**, 1086 (1978)- "Asymptotic Graph Counting Techniques in
*φ*Field Theory"^{2N}- C. M. Bender and W. E. Caswell
- Journal of Mathematical Physics
**19**, 2579 (1978)- "Asymptotic Graph Counting Techniques in
- "Resonance Calculations for Arbitrary Potentials"
- C. M. Bender, R. Yaris, J. Bendler, R. Lovett, and P. A. Fedders
- Physical Review A
**18**, 1816 (1978)- "Strong-Coupling Expansion in Quantum Field Theory"
- C. M. Bender, F. Cooper, G. S. Guralnik, and D. H. Sharp
- Physical Review D
**19**, 1865 (1979)- "Tight Upper and Lower Bounds on Perturbation Coefficients for Anharmonic Oscillators"
- C. M. Bender and K.-M. Ling
- Physical Review D
**18**, 3808 (1979)- "Multilegged Propagators in Strong-Coupling Expansions"
- C. M. Bender, F. Cooper, G. S. Guralnik, D. H. Sharp, and M. L. Silverstein
- Physical Review D
**20**, 1374 (1979)- "Improvement of an Extrapolation Scheme for Strong-Coupling Expansions in Quantum Field Theory"
- C. M. Bender, F. Cooper, G. S. Guralnik, R. Roskies, and D. H. Sharp
- Physical Review Letters
**43**, 537 (1979)- "WKB Approximation for Quantum Theory on a Lattice"
- C. M. Bender, G. S. Guralnik, and M. L. Silverstein
- Physical Review D
**20**, 2583 (1979)- "A Novel Approach to the Solution of Boundary-Layer Problems"
- C. M. Bender, F. Cooper, G. S. Guralnik, E. Mjolsness, H. Rose, and D. H. Sharp
- Advances in Applied Mathematics
**1**, 22 (1980)- "Strong Coupling Expansion for Classical Statistical Dynamics"
- C. M. Bender, F. Cooper, G. S. Guralnik, H. Rose, and D. H. Sharp
- Journal of Statistical Physics
**22**, 647 (1980)- "Effective Potential for a Renormalized
*d*-Dimensional*g*φ^{4}Field Theory in the*g*rightarrow infinity Limit"- C. M. Bender, F. Cooper, G. S. Guralnik, H. Moreno, R. Roskies, and D. H. Sharp
- Physical Review Letters
**45**, 501 (1980)- "Effective Potential for a Renormalized
- "Renormalizing the Strong-Coupling Expansion for Quantum Field Theory: Present Status"
- C. M. Bender, F. Cooper, G. S. Guralnik, R. Roskies, and D. H. Sharp
*Recent Developments in High-Energy Physics*,- Ed. by Behram Kursunoglu, Arnold Perlmutter, and Linda F. Scott
- (Plenum Publishing Corporation, New York, 1980), pp. 211-237
- "A Novel Approach to Boundary Layer Problems"
- C. M. Bender
- Los Alamos Science
**2**, 76 (1981)- "Strong-Coupling Expansion for the Effective Potential on a Lattice"
- C. M. Bender, F. Cooper, G. S. Guralnik, R. Roskies, and D. H. Sharp
- Physical Review D
**23**, 2976 (1981)- "Numerical Computation of the Renormalized Effective Potential in the Strong-Coupling Limit"
- C. M. Bender, F. Cooper, G. S. Guralnik, R. Roskies, and D. H. Sharp
- Physical Review D
**23**, 2999 (1981)- "Solution of General 1-Turning-Point Schroedinger Equation Using Lattice Extrapolation Techniques"
- C. M. Bender and D. H. Sharp
- Physical Review D
**24**, 1691 (1981)- "Strong-Coupling Expansion for the Ground-State Energy in the
*|x|*Potential"^{α}- C. M. Bender, L. R. Mead, and L. M. Simmons, Jr.
- Physical Review D
**24**, 2674 (1981)- "Strong-Coupling Expansion for the Ground-State Energy in the
- "Higher-Order Terms in the Strong-Coupling Expansion for the Renormalized Effective Potential"
- C. M. Bender, F. Cooper, G. S. Guralnik, R. Roskies, and D. H. Sharp
- Physical Review D
**24**, 2683 (1981)- "Continuum Regulation of the Strong-Coupling Expansion for Quantum Field Theory"
- C. M. Bender, F. Cooper, R. Kenway, and L. M. Simmons, Jr.
- Physical Review D
**24**, 2693 (1981)- "Perturbation Theory in Large Order for Some Elementary Systems"
- C. M. Bender
- Invited Talk Presented at the March 1981 Sanibel Symposium
- on Perturbation Theory in Large Order, Palm Coast, Florida.
- International Journal of Quantum Chemistry XXI, 93 (1982)
- "Semi-Classical Perturbation Theory for the Hydrogen Atom in a Uniform Magnetic Field"
- C. M. Bender, L. D. Mlodinow, and N. Papanicolaou
- Physical Review D
**25**, 1305 (1982)- "Effect of Renormalization on the Large-Order Behavior of Weak- and Strong-Coupling Perturbation Theory"
- C. M. Bender and R. Z. Roskies
- Physical Review D
**25**, 427 (1982)- "Problems with Continuum Regulation of Strong-Coupling Expansions"
- C. M. Bender, F. Cooper, R. D. Kenway, and L. M. Simmons, Jr.
- Physics Letters
**109B**, 63 (1982)- "Finite-Element Approximation in Quantum Field Theory"
- C. M. Bender, G. S. Guralnik, and D. H. Sharp
- Nuclear Physics
**B207**, 54 (1982)- "Lorentz Transformation Properties of Nonconserved Charges"
- C. M. Bender and D. A. Williams
- Journal of Mathematical Physics
**24**, 990 (1983)- "A New Strong-Coupling Expansion for Quantum Field Theory Based on the Langevin Equation"
- C. M. Bender, F. Cooper, and B. Freedman
- Nuclear Physics
**B219**, 61 (1983)- "New Test for Spontaneous Breakdown of Supersymmetry"
- C. M. Bender, F. Cooper, and A. Das
- Physical Review D
**28**, 1473 (1983)- "Two-Dimensional Steady-State Diffusion of a Passive Scalar in a Flow Field"
- C. M. Bender and L. Turner
- Journal of Mathematical Physics
**24**, 1630 (1983)- "Solution of Operator Field Equations by the Method of Finite Elements"
- C. M. Bender and D. H. Sharp
- Physical Review Letters
**50**, 1535 (1983)- "Large-Order Behavior of Lattice Strong-Coupling Expansions"
- C. M. Bender, L. R. Mead, and L. M. Simmons, Jr.
- Physical Review D
**28**, 936 (1983)- "Continuum Limit of Supersymmetric Field Theories on a Lattice"
- C. M. Bender, F. Cooper, and A. Das
- Physical Review Letters
**50**, 397 (1983)- "Failure of the Naive Loop Expansion for the Effective Potential in
*φ*Field Theory when There is Broken Symmetry"^{4}- C. M. Bender and F. Cooper
- Nuclear Physics
**B224**, 403 (1983)- "Failure of the Naive Loop Expansion for the Effective Potential in
- "Finite-Element Approximation in Quantum Theory"
- C. M. Bender
- Invited talk given at Conference on Non-Perturbative Quantum
- Chromodynamics, Oklahoma State University, March 1983, published in
*Proceedings of the Workshop on Non-Perturbative Quantum Chromodynamics*,- Ed. by K. A. Milton and M. A. Samuel (Birkhauser, Boston, 1983),
- pp. 155-167
- "Consistent Formulation of Fermions on a Minkowski Lattice"
- C. M. Bender, K. A. Milton, and D. H. Sharp
- Physical Review Letters
**51**, 1815 (1983)- "Finite-Element Approximation in Quantum Theory"
- C. M. Bender
- Invited Talk given at VII International Congress on Mathematical Physics,
- University of Colorado, Boulder, Colorado, June 1983,
- Physica
**124A**, 91 (1984)- "Strong-Coupling Approximation in Supersymmetric Field Theory"
- C. M. Bender, A. Das, H.-A. Lim, and L. M. Simmons, Jr.
- Physics Letters
**134B**, 225 (1984)- "Production, Decay, and Mixing Models of the Iota Meson"
- C. M. Bender, W. F. Palmer, and S. S. Pinsky
- Physical Review D
**30**, 1002 (1984)- "On Higher-Order Computations in Strong Coupling"
- C. M. Bender, A. Das, and H.-A. Lim
- Pramana
**23**, 695 (1984)- "Operator Lattices"
- C. M. Bender
- Published in
*Gauge Theory on a Lattice: 1984*- (a Workshop held at Argonne National Laboratory, April 1984),
- Ed. by C. Zachos, W. Celmaster, E. Kovacs, and D. Sivers
- (June 1984), pp. 230-241
- "Gauge Invariance and the Finite-Element Solution of the Schwinger Model"
- C. M. Bender, K. A. Milton, and D. H. Sharp
- Physical Review D
**31**, 383 (1985)- "Functional Differential Equation Approach to the Large
*N*Expansion and Mean Field Perturbation Theory"- C. M. Bender and F. Cooper
- Annals of Physics
**160**, 323 (1985)- "Functional Differential Equation Approach to the Large
- "High-Order Strong-Coupling Calculation of the Ground-State Energy Density in Supersymmetric Field Theory"
- C. M. Bender, P. H. Burchard, A. Das, H.-A. Lim, and J. A. Shapiro
- Physical Review Letters
**54**, 2481 (1985)- "Strong-Coupling Calculation of Mass Ratios in Supersymmetric Field Theory"
- C. M. Bender, A. Das, H.-A Lim, and L. M. Simmons, Jr.
- Physics Letters
**154B**, 381 (1985)- "Quantum Tunneling Using Discrete-Time Operator Difference Equations"
- C. M. Bender, F. Cooper, J. E. O'Dell, and L. M. Simmons, Jr.
- Physical Review Letters
**55**, 901 (1985)- "A Proposal for the Solution of Quantum Field Theory Problems Using a Finite-Element Approximation"
- C. M. Bender
- Published in
*Applications of Computer Algebra*(Proceedings of the American- Chemical Society Meeting, Philadelphia, August 1984), Ed. by R. Pavelle
- (Kluwer-Nijhoff, Boston, 1985), pp. 392-406
- "Discrete-Time Quantum Mechanics"
- C. M. Bender, K. A. Milton, D. H. Sharp, L. M. Simmons, Jr., and R. Stong
- Physical Review D
**32**, 1476 (1985)- "A Simple Approach to Tunneling Using the Method of Finite Elements"
- C. M. Bender, F. Cooper, V. P. Gutschick, and M. M. Nieto
- Physical Review D
**32**, 1486 (1985)- "Tunneling and the Low-Momentum Expansion of the Effective Action"
- C. M. Bender, F. Cooper, B. Freedman, and R. W. Haymaker
- Nuclear Physics
**B 256**, 653 (1985)- "Resonances in Quantum Mechanical Tunneling"
- M. M. Nieto, V. P. Gutschick, C. M. Bender, F. Cooper, and D. Strottman
- Physics Letters B
**163**, 336 (1985)- "Relativistic Brachistochrone"
- C. M. Bender and H. F. Goldstein
- Journal of Mathematical Physics
**27**, 507 (1986)- "Discrete-Time Quantum Mechanics. II. Systems with Several Degrees of Freedom"
- C. M. Bender, K. A. Milton, S. S. Pinsky, and L. M. Simmons, Jr.
- Physical Review D
**33**, 1692 (1986)- "The Method of Finite Elements, Path Integrals, and Quantum Field Theory"
- C. M. Bender, G. S. Guralnik, and D. H. Sharp
- Invited paper in
*Science and Computers, A Volume Dedicated to Nicolas**Metropolis*, Ed. by Gian-Carlo Rota,- Advances in Mathematics Supplementary Studies
**10**, 321 (1986)- "Matrix Methods for the Finite-Element Approximation in Quantum Mechanics"
- C. M. Bender, L. M. Simmons, Jr., and R. Stong
- Physical Review D
**33**, 2362 (1986)- "Resolution of the Operator-Ordering Problem Using the Method of Finite Elements"
- C. M. Bender, L. R. Mead, and S. S. Pinsky
- Physical Review Letters
**56**, 2445 (1986)- "Accurate Determination of Spectra in Discrete-Time Quantum Mechanics"
- C. M. Bender and M. L. Green
- Physical Review D
**34**, 3255 (1986)- "Approximate Determination of Mass Gap in Quantum Field Theory Using the Method of Finite Elements"
- C. M. Bender and K. A. Milton
- Physical Review D
**34**, 3149 (1986)- "Quantum Systems on a Lattice"
- C. M. Bender
- Published in
*Path Integrals from meV to MeV*(Selected papers from the- Symposium held at the Bielefeld Center for Interdisciplinary Research, August
- 1985), Ed. by M. C. Gutzwiller, A. Inomata, J. R. Klauder, and L. Streit
- (World Scientific, Singapore, 1986), pp. 33-49
- "The Iota Glueball"
- W. F. Palmer, S. S. Pinsky, and C. M. Bender
- Published in
*New Particle Production, La Plagne, 1984*- Proceedings of the 1984 La Plagne Meeting (published in 1986), pp. 749-757
- "Maximum Entropy Summation of Divergent Series"
- C. M. Bender, L. R. Mead, and N. Papanicolaou
- Journal of Mathematical Physics
**28**, 1016 (1987)- "Finite-Element Approximation in Quantum Field Theory"
- C. M. Bender
- Invited talk presented at the Seventh Vanderbilt High Energy Physics
- Conference, Published in
*Quarks, Strings, Dark Matter, and all the rest*,- Ed. by R. S. Panvini and T. J. Weiler
- (World Scientific Publishing, Singapore, 1987), pp. 25-41
- "Continuous Hahn Polynomials and the Heisenberg Algebra"
- C. M. Bender, L. R. Mead, and S. S. Pinsky
- Journal of Mathematical Physics
**28**, 509 (1987)- "Discrete-Time Quantum Mechanics. III. Spin Systems"
- C. M. Bender, F. Cooper, K. A. Milton, S. S. Pinsky, and L. M. Simmons, Jr.
- Physical Review D
**35**, 3081 (1987)- "Logarithmic Approximations to Polynomial Lagrangians"
- C. M. Bender, K. A. Milton, M. Moshe, S. S. Pinsky, and L. M. Simmons, Jr.
- Physical Review Letters
**58**, 2615 (1987)- "Formulation of Quantum Theory on a Minkowski Space-Time Lattice"
- C. M. Bender
- Published in
*String Theory - Quantum Gravity and Quantum Cosmology**(Integrable and Conformal Invariant Theories),*- (Proceedings of the Paris-Meudon Colloquium, Meudon, France, September
- 1986), Ed. by H. De Vega and N. Sanchez (World Scientific, Singapore, 1987),
- pp. 465-484
- "Novel Perturbative Scheme in Quantum Field Theory"
- C. M. Bender, K. A. Milton, M. Moshe, S. S. Pinsky, and L. M. Simmons, Jr.
- Physical Review D
**37**, 1472 (1988)- "Exact Operator Solutions to Euler Hamiltonians"
- C. M. Bender G. V. Dunne
- Physics Letters
**B 200**, 520 (1988)- "WKB Calculation of Quantum Adiabatic Phases and Nonadiabatic Corrections"
- C. M. Bender and N. Papanicolaou
- Journal de Physique
**49**, 561 (1988)- "A New Perturbative Approximation Applied to Supersymmetric Quantum Field Theory"
- C. M. Bender, K. A. Milton, S. S. Pinsky, and L. M. Simmons, Jr.
- Physics Letters
**B 205**, 493 (1988)- "New Nonperturbative Calculation: Renormalization and the Triviality of
*(λ φ*Field Theory"^{4})_{4}- C. M. Bender and H. F. Jones
- Physical Review D
**38**, 2526 (1988)- "New Nonperturbative Calculation: Renormalization and the Triviality of
- "New Perturbative Calculation of the Fermion-Boson Mass Ratio in a Supersymmetric Quantum Field Theory"
- C. M. Bender and K. A. Milton
- Physical Review D
**38**, 1310 (1988)- "Polynomials and Operator Orderings"
- C. M. Bender and G. V. Dunne
- Journal of Mathematical Physics
**29**, 1727 (1988)- "Nonperturbative Perturbation Theory"
- C. M. Bender
- Published in
*Hadron Structure '87*(Proceedings of the conference Hadron- Structure '87, Smolenice, Czechoslovakia, November 1987), Ed. by D. Krupa
- (Slovak Academy of Sciences, Bratislava, 1988)
- Physics and Applications, Vol. 14
- "Evaluation of Feynman Diagrams in the Logarithmic Approach to Quantum Field Theory"
- C. M. Bender and H. F. Jones
- Journal of Mathematical Physics
**29**, 2659 (1988)- "Nonunique Solution to the Schwinger-Dyson Equations"
- C. M. Bender, F. Cooper, and L. M. Simmons, Jr.
- Physical Review D
**39**, 2343 (1989)- "A New Perturbative Approach to Nonlinear Problems"
- C. M. Bender, K. A. Milton, S. S. Pinsky, and L. M. Simmons, Jr.
- Journal of Mathematical Physics
**30**, 1447 (1989)- "The delta Expansion for Stochastic Quantization"
- C. M. Bender, F. Cooper, and K. A. Milton
- Physical Review D
**39**, 3684 (1989)- "Exact Solutions to Operator Differential Equations"
- C. M. Bender and G. V. Dunne
- Physical Review D
**40**, 2739 (1989)- "Nonperturbative Perturbation Theory"
- C. M. Bender
- Invited talk presented at the IV International Workshop on Recent
- Developments in High Energy Physics, Kolymbari, Crete (July, 1988)
- Nuclear Physics B (Proc. Suppl.)
**11**, 316 (1989)- "The delta Expansion and Local Gauge Invariance"
- C. M. Bender, F. Cooper, and K. A. Milton
- Physical Review D
**40**, 1354 (1989)- "Novel Perturbative Scheme in Quantum Field Theory"
- C. M. Bender
- Published in
*Hadron Interactions*(Proceedings of the International Symposium- "Hadron Interactions - Theory and Phenomenology," Bechyne Castle,
- Czechoslovakia, June 1988), Ed. by J. Fischer, P. Kolar, and V. Kundrat
- (Czechoslovak Academy of Sciences, Prague, 1989)
- "Concluding Talk"
- C. M. Bender
- Published in
*Hadron Interactions*(Proceedings of the International Symposium- "Hadron Interactions - Theory and Phenomenology," Bechyne Castle,
- Czechoslovakia, June 1988), Ed. by J. Fischer, P. Kolar, and V. Kundrat
- (Czechoslovak Academy of Sciences, Prague, 1989), pp. 749-757
- "A Simple Classical Model of Dynamical Symmetry Breaking"
- C. M. Bender and F. Cooper
- LA-UR-89-2693, unpublished (1989)
- "Integration of Operator Differential Equations"
- C. M. Bender and G. V. Dunne
- Physical Review D
**40**, 3504 (1989)- "Matched Asymptotic Expansions: Ideas and Techniques" (Book review)
- C. M. Bender
- Physics Today
**42**, 72 (July, 1989)- "Exact Solutions to Operator Differential Equations"
- C. M. Bender
- Invited talk published in
*Proceedings of the XXIII International Symposium at**Ahrenshoop*, GDR, October, 1989, Ed. by H. J. Kaiser- (Academy of Sciences of the GDR, Zeuthen, 1989), pp. 91-105
- "New Approach to the Solution of Nonlinear Problems"
- C. M. Bender
- Invited talk published in
*Proceedings of the XXIII International Symposium at**Ahrenshoop*, GDR, October, 1989, Ed. by H. J. Kaiser- (Academy of Sciences of the GDR, Zeuthen, 1989), pp. 106-125
- "delta expansion for a Quantum Field Theory in the Nonperturbative Regime"
- C. M. Bender, K. A. Milton, S. S. Pinsky, and L. M. Simmons, Jr.
- Journal of Mathematical Physics
**31**, 2722 (1990)- "Derivative Expansions for Affinely Quantized Field Theories"
- C. M. Bender, R. J. Rivers, and C. C. Wong
- Physical Review D
**41**, 455 (1990)- "Hot Delta Expansion"
- C. M. Bender and T. Rebhan
- Physical Review D
**41**, 3269 (1990)- "Nonperturbative Square-Well Approximation to a Quantum Theory"
- C. M. Bender and S. Boettcher
- Journal of Mathematical Physics
**31**, 2579 (1990)- "A New Perturbative Approach to Nonlinear Partial Differential Equations"
- C. M. Bender, S. Boettcher, and K. A. Milton
- Journal of Mathematical Physics
**32**, 3031 (1991)- "Covariance of the Gauge Field in Three-Dimensional Quantum Electrodynamics"
- C. M. Bender and G. V. Dunne
- Physical Review D
**44**, 2565 (1991)- "Solution of Operator Equations of Motion"
- C. M. Bender
- Invited talk at the Liblice Conference held by the Czechoslovak
- Academy of Sciences in June 10-15, 1990
- Published in
*Rigorous Results in Quantum Dynamics,*Ed. by J. Dittrich and- P. Exner (World Scientific, Singapore, 1991), pp. 99-112
- "New Approach to the Solution of Nonlinear Problems"
- C. M. Bender
- Invited talk published in the proceedings of the 1991 Workshop
*Large Scale Structures in Nonlinear Physics*,- held in Villefranche-sur-Mer, January, 1991.
- Published in Lecture Notes in Physics No. 392, Ed. by J.-D. Fournier and
- P.-L. Sulem (Springer-Verlag, Berlin, 1991), pp. 190-210.
- "Novel Perturbation Expansion for the Langevin Equation"
- C. M. Bender, F. Cooper, G. Kilkup, P. Roy, and L. M. Simmons, Jr.
- Journal of Statistical Physics
**64**, 395 (1991)- "delta Expansion Applied to Quantum Electrodynamics"
- C. M. Bender, S. Boettcher, and K. A. Milton
- Physical Review D
**45**, 639 (1992)- "delta Expansion for Local Gauge Field Theories. I. A One-Dimensional Model"
- C. M. Bender, F. Cooper, K. A. Milton, M. Moshe, S. S. Pinsky, and
- L. M. Simmons, Jr.
- Physical Review D
**45**, 1248 (1992)- "Taylor Series and delta-Perturbation Expansions for a Nonlinear Semiconductor Transport Equation"
- B. Abraham-Shrauner, C. M. Bender, and R. N. Zitter
- Journal of Mathematical Physics
**33**, 1335 (1992)- "delta Expansion for Local Gauge Field Theories. II. Nonperturbative Calculation of the Anomaly in the Schwinger Model"
- C. M. Bender, K. A. Milton, and M. Moshe
- Physical Review D
**45**, 1261 (1992)- "Derivative Expansions for Affinely-Quantized Field Theories. II. Scale-Invariant Quantization"
- R. J. Rivers, C. C. Wong, and C. M. Bender
- Physical Review D
**45**, 4600 (1992)- "Dimensional Expansions"
- C. M. Bender, S. Boettcher, and L. Lipatov
- Physical Review Letters
**68**, 3674 (1992)- "Almost Zero-Dimensional Quantum Field Theories"
- C. M. Bender, S. Boettcher, and L. Lipatov
- Physical Review D
**46**, 5557 (1992)- "Analytic Continuation of Eigenvalue Problems"
- C. M. Bender and A. Turbiner
- Physics Letters
**A 173**, 442 (1993)- "Spontaneous Symmetry Breaking in
*φ*in Light-Front Field Theory"_{1+1}^{4}- C. M. Bender, S. Pinsky, and B. Van de Sande
- Physical Review D
**48**, 816 (1993)- "Spontaneous Symmetry Breaking in
- "Dimensional Expansions"
- C. M. Bender
- Talk given at the Division of Particles and Fields 1992 meeting of the
- American Physical Society held in Chicago, Illinois,
- Published in
*The Fermilab Meeting DPF 92*,- (World Scientific, Singapore, 1993), Vol. 2, pp. 1549-1551.
- "Dimensional Expansion for the Ising Limit of Quantum Field Theory"
- C. M. Bender and S. Boettcher
- Physical Review D
**48**, 4919 (1993)- "Exact Solutions to Operator Differential Equations"
- C. M. Bender
- Invited talk published in the proceedings of the special session on Lie
- Algebras, Cohomology, and New Applications in Quantum Mechanics of the
- 1992 Mathematical Society meeting held in Springfield, Missouri.
- Contemporary Mathematics
**160**, 31 (1994)- "Determination of
*f(infinity)*from the Asymptotic Series for*f(x)*about*x=0*"- C. M. Bender and S. Boettcher
- Journal of Mathematical Physics
**35**, 1914 (1994)- "Determination of
- "Random Walks in Noninteger Dimension"
- C. M. Bender, S. Boettcher, and L. R. Mead
- Journal of Mathematical Physics
**35**, 368 (1994)- "Continued Fraction as a Discrete Nonlinear Transform"
- C. M. Bender and K. A. Milton
- Journal of Mathematical Physics
**35**, 364 (1994)- "Discrete-Time Quantum Mechanics"
- C. M. Bender, L. R. Mead, and K. A. Milton
- Computers and Mathematics with Applications
**28**, 279 (1994)- "Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions"
- C. M. Bender, A. Duncan, and H. F. Jones
- Physical Review D
**49**, 4219 (1994)- "Spherically-Symmetric Random Walks in Noninteger Dimension"
- C. M. Bender, S. Boettcher, and M. Moshe
- Journal of Mathematical Physics
**35**, 4941 (1994)- "Eleventh-Order Calculation of Ising-Limit Green's Functions for Scalar Quantum Field Theory in Arbitrary Space-Time Dimension
*D*"- C. M. Bender and S. Boettcher
- Physical Review D
**51**, 1875 (1994)- "Eleventh-Order Calculation of Ising-Limit Green's Functions for Scalar Quantum Field Theory in Arbitrary Space-Time Dimension
- "Scalar Casimir Effect for a
*D*-Dimensional Sphere"- C. M. Bender and K. A. Milton
- Physical Review D
**50**, 6547 (1994)- "Scalar Casimir Effect for a
- "Eigenvalue Integro-Differential Equations for Orthogonal Polynomials on the Real Line"
- C. M. Bender and J. Feinberg
- Journal of Mathematical Physics
**36**, 3106 (1995)- "
*D*-Dimensional Moments of Inertia"- C. M. Bender and L. R. Mead
- American Journal of Physics
**63**, 1011 (1995)- "
- "Universality in Random Walks with Birth and Death"
- C. M. Bender, S. Boettcher, and P. N. Meisinger
- Physical Review Letters
**75**, 3210 (1995)- "Spherically Symmetric Random Walks I. Representation in Terms of Orthogonal Polynomials"
- C. M. Bender, F. Cooper, and P. N. Meisinger
- Physical Review E
**54**, 100 (1996)- "Spherically Symmetric Random Walks II. Dimensionally Dependent Critical Behavior"
- C. M. Bender, S. Boettcher, and P. N. Meisinger
- Physical Review E
**54**, 112 (1996)- "Spherically Symmetric Random Walks III. Polymer Adsorption at a Hyperspherical Boundary"
- C. M. Bender, S. Boettcher, and P. N. Meisinger
- Physical Review E
**54**, 127 (1996)- "Summation of Power Series by Continued Exponentials"
- C. M. Bender and J. P. Vinson
- Journal of Mathematical Physics
**37**, 4103 (1996)- "Quasi-Exactly Solvable Systems and Orthogonal Polynomials"
- C. M. Bender and G. V. Dunne
- Journal of Mathematical Physics
**37**, 6 (1996)- "Theoretical Physics"
- C. M. Bender
- Invited contribution to the Macmillan Encyclopedia of Physics
- (Simon and Schuster Macmillan, New York, 1996), pp. 1585-1588
- "Multiple-Scale Analysis of the Quantum Anharmonic Oscillator"
- C. M. Bender and L. M. A. Bettencourt
- Physical Review Letters
**77**, 4114 (1996)- "Multiple-Scale Analysis of Quantum Systems"
- C. M. Bender and L. M. A. Bettencourt
- Physical Review D
**54**, 7710 (1996)- "Nonperturbative Calculation of Symmetry Breaking in Quantum Field Theory"
- C. M. Bender and K. A. Milton
- Physical Review D
**55**, R3255 (1997)- "Dimensional Expansion as a Nonperturbative Approach to Quantum Field Theory"
- C. M. Bender
- Invited talk published in the proceedings of Workshop on Quantum
- Chromodynamics: Confinement, Collisions, and Chaos,
- held at the American University of Paris, June 1996
- Ed. by H. M. Fried and B. Muller
- (World Scientific, Singapore, 1997), pp. 82-88
- "Semiclassical Analysis of Quasi-Exact Solvability"
- C. M. Bender, G. V. Dunne, and M. Moshe
- Physical Review A
**55**, 2625 (1997)- "Continuum Limit of Lattice Approximation Schemes"
- C. M. Bender and A. Tovbis
- Journal of Mathematical Physics
**38**, 3700 (1997)- "Quasi-Exactly Solvable Quartic Potential"
- C. M. Bender and S. Boettcher
- Journal of Physics A: Mathematical and General
**31**, L273 (1998)- "Model of Supersymmetric Quantum Field Theory with Broken Parity Symmetry"
- C. M. Bender and K. A. Milton
- Physical Review D
**57**, 3595 (1998)- "Real Spectra in Non-Hermitian Hamiltonians Having
**PT**Symmetry"- C. M. Bender and S. Boettcher
- Physical Review Letters
**80**, 5243-5246 (1998)- "Real Spectra in Non-Hermitian Hamiltonians Having
- "Pre-Eruptive Behavior of Oblong Geyser"
- C. M. Bender and D. E. Bender
- GOSA Transactions
**6**, 21 (1998)- "The Complex Pendulum"
- C. M. Bender
- Invited talk published in the proceedings of the conference
- Particles, Fields & Gravitation '98
- held at the University of Lodz, Poland, April 1998
- AIP Conference Proceedings 453, Ed. by J. Rembielinski
- (American Institute of Physics, New York, 1998), pp. 167-176
- "Complex Periodic Potentials with Real Band Structure"
- C. M. Bender, G. V. Dunne, and P. N. Meisinger
- Physics Letters A
**252**, 272-276 (1999) [arXiv: cond-mat/9810369]- "
**PT**-Symmetric Quantum Mechanics"- C. M. Bender, S. Boettcher, and P. N. Meisinger
- Journal of Mathematical Physics
**40**, 2201-2229 (1999) [arXiv: quant-ph/9809072]- "
- "The Complex Pendulum"
- C. M. Bender
- Invited talk at the Memorial Symposium in honor of Richard Slansky,
- Los Alamos National Laboratory, May 1998
- Physics Reports
**315**, 27-40 (1999)- "Non-Hermitian Quantum Field Theory"
- C. M. Bender
- Invited talk published in the proceedings of the
- Fourth Workshop on Quantum Chromodynamics
- held at the American University of Paris, June 1998
- Ed. by H. M. Fried and B. Muller
- (World Scientific, Singapore, 1999), pp. 435-444
- "A Nonunitary Version of Massless Quantum Electrodynamics Possessing a Critical Point"
- C. M. Bender and K. A. Milton
- Journal of Physics A: Mathematical and General
**32**, L87-L92 (1999)- "Dimensional Expansion for the Delta Function Potential"
- C. M. Bender and L. R. Mead
- European Journal of Physics
**20**, 117-121 (1999)- "Quantum Field Theory of Partitions"
- C. M. Bender, D. C. Brody, and B. K. Meister
- Journal of Mathematical Physics
**40**, 3239 (1999)- "Large-Order Perturbation Theory for a Non-Hermitian
**PT**-Symmetric Hamiltonian"- C. M. Bender and G. V. Dunne
- Journal of Mathematical Physics
**40**, 4616 (1999)- "Large-Order Perturbation Theory for a Non-Hermitian
- "Variational Ansatz for
**PT**-Symmetric Quantum Mechanics"- C. M. Bender, F. Cooper, P. N. Meisinger, and V. M. Savage
- Physics Letters A
**259**, 224-231 (1999)- "Variational Ansatz for
- "Complex Square Well -- A New Exactly Solvable Quantum-Mechanical Model"
- C. M. Bender, S. Boettcher, H. F. Jones, and V. M. Savage
- Journal of Physics A: Mathematical and General
**32**, 6771-6781 (1999)- "Effective Potential for
**PT**-Symmetric Quantum Field Theories"- C. M. Bender and H. F. Jones
- Foundations of Physics
**30**, 393-412 (2000)- "Effective Potential for
- "Quantum-Mechanical Carnot Engine"
- C. M. Bender, D. C. Brody, and B. K. Meister
- Journal of Physics A: Mathematical and General
**33**, 4427 (2000) [arXiv: quant-ph/0007002]- "Conjecture on the Interlacing of Zeros in Complex Sturm-Liouville Problems"
- C. M. Bender, S. Boettcher, and V. M. Savage
- Journal of Mathematical Physics
**41**, 6381-87 (2000)- "Underdetermined Systems of Partial Differential Equations"
- C. M. Bender, G. V. Dunne, and L. R. Mead
- Journal of Mathematical Physics
**41**, 6388-98 (2000)- "Solution of Schwinger-Dyson Equations for
**PT**-Symmetric Quantum Field Theory"- C. M. Bender, K. A. Milton, and V. M. Savage
- Physical Review D
**62**, 085001 (2000)- "Solution of Schwinger-Dyson Equations for
- "Combinatorics and Field Theory"
- C. M. Bender, D. C. Brody, and B. K. Meister
- Twistor Newsletter
**45**, 36-39 (2000)- "Calculation of the One-Point Green's Function for a
*-g φ*Quantum Field Theory"^{4}- C. M. Bender, P. N. Meisinger, and H. Yang
- Physical Review D
**63**, 45001 (2001)- "Calculation of the One-Point Green's Function for a
- "Comment on a Recent Paper by Mezincescu"
- C. M. Bender and Q. Wang
- Journal of Physics A: Mathematical and General
**34**, 3325 (2001)- "Conjecture on the Reality of Spectra of Non-Hermitian Hamiltonians"
- C. M. Bender, S. Boettcher, and P. N. Meisinger
- Published in
*Fluctuating Paths and Fields*(World Scientific, Singapore, 2001), pp. 105-115- Festschrift Dedicated to Hagen Kleinert on the Occasion of His 60th Birthday
- "Double-Scaling Limit of a Broken Symmetry Quantum Field Theory in Dimensions
*D*<2"- C. M. Bender, S. Boettcher, H. F. Jones, and P. N. Meisinger
- Journal of Mathematical Physics
**42**, 1960-1973 (2001)- "Double-Scaling Limit of a Broken Symmetry Quantum Field Theory in Dimensions
- "Bound States of Non-Hermitian Quantum Field Theories"
- C. M. Bender, S. Boettcher, H. F. Jones, P. N. Meisinger, and M. Simsek
- Physics Letters A
**291**, 197-202 (2001)- "Numerical Evidence that the Perturbation Expansion for a Non-Hermitian
**PT**-symmetric Hamiltonian is Stieltjes"- C. M. Bender and E. J. Weniger
- Journal of Mathematical Physics
**42**, 2167-2183 (2001)- "Numerical Evidence that the Perturbation Expansion for a Non-Hermitian
- "Complex WKB Analysis of Energy-Level Degeneracies of Non-Hermitian Hamiltonians"
- C. M. Bender, M. Berry, P. N. Meisinger, V. M. Savage, and M. Simsek
- Journal of Physics A: Mathematical and General
**34**, L31-L36 (2001)- "A Class of Exactly-Solvable Eigenvalue Problems"
- C. M. Bender and Q. Wang
- Journal of Physics A: Mathematical and General
**34**, 9835-9847 (2001)- "Quantum Complex Henon-Heiles Potentials"
- C. M. Bender, G. V. Dunne, P. N. Meisinger, and M. Simsek
- Physics Letters A
**281**, 311-316 (2001)- "Perturbation Theory"
- C. M. Bender
- Published in
*Encyclopedia of Physical Science and Technology*,- 3rd edition (Academic Press, New York, 2001)
- "Complex Extension of Quantum Mechanics"
- C. M. Bender, D. C. Brody, and H. F. Jones
- Physical Review Letters
**89**, 270401 (2002)- "Entropy and Temperature of a Quantum Carnot Engine"
- C. M. Bender, D. C. Brody, and B. K. Meister
- Proceedings of the Royal Society of London A
**458**, 1519-1526 (2002)- "Generalized
**PT**Symmetry and Real Spectra"- C. M. Bender, M. V. Berry, and A. Mandilara
- Journal of Physics A: Mathematical and General
**35**, L467-L471 (2002)- "Generalized
- "Non-Hermitian Hamiltonians Having Real Spectra"
- C. M. Bender
- Invited talk published in the proceedings of the
- Sixth Workshop on Quantum Chromodynamics
- held at the American University of Paris, June 2001
- Ed. by H. M. Fried, Y. Gabellini, and B. Muller
- (World Scientific, Singapore, 2002), pp. 181-188
- "Complex Hamiltonians Having Real Spectra"
- C. M. Bender
- Invited talk published in the proceedings of the
- Second International Symposium: Quantum Theory and Symmetries
- Krakow, July 2001
- Ed. by E. Kapuscik and A. Horzela
- (World Scientific, Singapore, 2002), pp. 11-19
- "Unusual Eigenvalue Problems"
- C. M. Bender
- Invited talk published in the proceedings of the
- Second International Symposium: Quantum Theory and Symmetries
- Krakow, July 2001
- Ed. by E. Kapuscik and A. Horzela
- (World Scientific, Singapore, 2002), pp. 291-304
- "Inverse of the
**PCT**Theorem"- C. M. Bender
- Invited talk published in the proceedings of the
- International Europhysics Conference on High Energy Physics
- Budapest, Hungary, July 2001
- Ed. by Andras Patkos, Peter Levai, and Simona Cerrato
- Proceedings of the Journal of High Energy Physics PRHEP-hep2001/232
- "Inverse of the
- "Boundary-Layer Theory, Strong-Coupling Series, and Large-Order Behavior"
- C. M. Bender, A. Pelster, and F. Weissbach
- Journal of Mathematical Physics
**43**, 4202-4220 (2002)- "Two-Point Green's Function in Non-Hermitian Quantum Field Theories"
- C. M. Bender, S. Boettcher, P. N. Meisinger, and Q. Wang
- Physics Letters A
**302**, 286-290 (2002)- "On Powers of Bessel Functions"
- C. M. Bender, D. C. Brody, and B. K. Meister
- Journal of Mathematical Physics
**44**, 309-314 (2003)- "Must a Hamiltonian be Hermitian?"
- C. M. Bender, D. C. Brody, and H. F. Jones
- American Journal of Physics
**71**, 1095-1102 (2003)- "All Hermitian Hamiltonians Have Parity"
- C. M. Bender, P. N. Meisinger, and Q. Wang
- Journal of Physics A: Mathematical and General
**36**, 1029-1031 (2003)- "Calculation of the Hidden Symmetry Operator in
**PT**-Symmetric Quantum Mechanics"- C. M. Bender, P. N. Meisinger, and Q. Wang
- Journal of Physics A: Mathematical and General
**36**, 1973-1983 (2003) [arXiv: quant-ph/0211166]- "Calculation of the Hidden Symmetry Operator in
- "Finite-Dimensional
**PT**-Symmetric Hamiltonians"- C. M. Bender, P. N. Meisinger, and Q. Wang
- Journal of Physics A: Mathematical and General
**36**, 6791-6797 (2003)- "Finite-Dimensional
- "So, Why Must a Hamiltonian be Hermitian?"
- C. M. Bender
- Plenary talk published in the proceedings of the
- Seventh Workshop on Quantum Chromodynamics
- held in Villefranche-sur-Mer, France, January 2003
- Ed. by H. M. Fried, Y. Gabellini, and B. Muller
- (World Scientific, Singapore, 2003), pp. 284-294
- "Properties of Non-Hermitian Quantum Field Theories"
- C. M. Bender
- Invited plenary talk published in the proceedings of the
- XXIV International Colloquium on Group Theoretical Methods in Physics
- Paris, France, July 2002
- Ed. by Jean-Pierre Gazeau and Richard Kerner,
- Institute of Physics (Bristol) Conference Series Number 173, 43-50 (2003)
- "Properties of Non-Hermitian Quantum Field Theories"
- C. M. Bender
- Invited plenary talk published in the proceedings of
- Singularities, Differential Equations and Mathematical Aspects of
- Quantum Physics: a Colloquium in Honor of Frederic Pham
- Nice, France, July 2002
- Ed. by Philippe Maisonobe and Michel Merle,
- Ann. Inst. Fourier, Grenoble
**53**, 997-1008 (2003)- "Quantized Three-Pillar Problem"
- C. M. Bender, D. C. Brody, and B. K. Meister
- preprint quant-ph/0302097
- "Semiclassical Calculation of the C Operator in
**PT**-Symmetric Quantum Mechanics"- C. M. Bender and H. F. Jones
- hep-th/0405113
- Physics Letters A
**328**, 102 (2004)- "Semiclassical Calculation of the C Operator in
- "What is the Optimal Shape of a City?"
- C. M. Bender, M. A. Bender, E. D. Demaine, S. P. Fekete
- Journal of Physics A: Mathematical and General
**37**, 147-159 (2004)- See this site for a popular description of this paper
- "
**PT**Symmetry in Quantum Field Theory"- C. M. Bender
- Plenary talk published in the proceedings of the Workshop
- Pseudo-Hermitian Hamiltonians in Quantum Physics,
- held in Prague, June 2003
- Ed. by M. Znojil
- Czechoslovak Journal of Physics
**54**, 13-28 (2004)- "
- "Greetings from the New Editor-in-Chief"
- C. M. Bender
- Journal of Physics A: Mathematical and General
**37**, Editorial (2004)- "Calculating the C Operator in
**PT**-Symmetric Quantum Mechanics"- C. M. Bender
- Plenary talk published in the proceedings of the Workshop
- Pseudo-Hermitian Hamiltonians in Quantum Physics II,
- held in Prague, June 2004
- Ed. by M.~Znojil
- Czechoslovak Journal of Physics
**54**, 1027-1038 (2004)- "Calculating the C Operator in
- "Scalar Quantum Field Theory with Complex Cubic Interaction"
- C. M. Bender, D. C. Brody, and H. F. Jones
- Physical Review Letters
**93**, 251601 (2004) [arXiv: hep-th/0402011]- "The C Operator in
**PT**-Symmetric Quantum Theories"- C. M. Bender, J. Brod, A. Refig, and M. E. Reuter
- Journal of Physics A: Mathematical and General
**37**, 10139-10165 (2004)- "The C Operator in
- "Extension of
**PT**-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction"- C. M. Bender, D. C. Brody, and H. F. Jones
- hep-th/0402183
- Physical Review D
**70**, 025001 (2004)- "Extension of
- "Complex Extension of Quantum Mechanics"
- C. M. Bender
- Plenary talk published in the Proceedings of the Fifth International Conference
- "Symmetry in Nonlinear Mathematical Physics," Kiev, June 2003
- Ed. by A. G. Nikitin, V. M. Boyko, R. O. Popovych and I. A. Yehorchenko
- Proceedings of the Institute of Mathematics of NAS of Ukraine,
- Vol. 50, part 2, pp. 617-628 (2004)
- "Ghost Busting:
**PT**-Symmetric Interpretation of the Lee Model"- C. M. Bender, S. F. Brandt, J.-H. Chen, and Q. Wang
- Physical Review D
**71**, 025014 (2005), [arXiv: hep-th/0411064]- "Ghost Busting:
- "The C Operator in
**PT**-Symmetric Quantum Field Theory Transforms as a Lorentz Scalar"- C. M. Bender, S. F. Brandt, J.-H. Chen, and Q. Wang
- Physical Review D
**71**, 065010 (2005) [arXiv: hep-th/0412316]- "The C Operator in
- "Continuum Limit of Lattice Approximation Schemes"
- C. M. Bender
- Plenary talk published in the proceedings of the Workshop on
- Group Theory and Numerical Methods
- held in Montreal, Canada, May 2003
- Ed. by D. Gomez-Ullate and A. Montpetit
- CRM Proceedings and Lecture Notes (co-published by the
- American Mathematical Society)
**39**, 33-48 (2005)- "Unusual Quantum States: Nonlocality, Entropy, Maxwell's Daemon, and Fractals"
- C. M. Bender, D. C. Brody, and B. K. Meister
- Proceedings of the Royal Society A
**461**, 733-753 (2005)- "Non-Hermitian Quantum Field Theory"
- C. M. Bender
- Plenary talk published in the proceedings of the Eighth Workshop
- on Quantum Chromodynamics held in Paris, France, June 2004
- Ed. by B. Muller and C.-I Tan
- International Journal of Modern Physics A
**20**, 4646-4652 (2005)- "Wilson Polynomials and the Lorentz Transformation Properties of the Parity Operator"
- C. M. Bender, P. N. Meisinger, and Q. Wang
- Journal of Mathematical Physics
**46**, 052302 (2005) [arXiv: math-ph/0412001]- "Introduction to
**PT**-Symmetric Quantum Theory"- C. M. Bender
- Invited paper in Contemporary Physics
**46**, 277 (2005) [arXiv: quant-ph/0501052]- "Introduction to
- "Quantum Mechanics Based on Non-Hermitian Hamiltonians"
- C. M. Bender
- Plenary talk published in the proceedings of the International Conference
- "Recent Trends in Exponential Asymptotics," Kyoto, July, 2004
- Ed. by Y. Takei
- RIMS Kokyuroku Symposium Series
**1424**, 64 (2005)- "New Quasi-Exactly Solvable Sextic Polynomial Potentials"
- C. M. Bender and M. Monou
- Journal of Physics A: Mathematical and General
**38**, 2179-2187 (2005) [arXiv: quant-ph/0501053]- "Bernoulli-like Polynomials Associated with Stirling Numbers"
- C. M. Bender, D. C. Brody, and B. K. Meister
- arXiv: math-ph/0509008
- "Reflectionless Potentials and
**PT**Symmetry"- Z. Ahmed, C. M. Bender, and M. V. Berry
- Journal of Physics A: Mathematical and General
**38**, L627-L630 (2005) [arXiv: quant-ph/0508117]- "Reflectionless Potentials and
- "Dual
**PT**-Symmetric Quantum Field Theories"- C. M. Bender, H. F. Jones and R. J. Rivers
- Physics Letters B
**625**, 333-340 (2005) [arXiv: hep-th/0508105]- "Dual
- "
**PT**-Symmetric Quantum Electrodynamics"- C. M. Bender, I. Cavero-Pelaez, K. A. Milton, and K. V. Shajesh
- Physics Letters B
**613**, 97 (2005) [arXiv: hep-th/0501180]- "
- "Ghost Busting: Making Sense of Non-Hermitian Hamiltonians"
- C. M. Bender
- Plenary talk published in the proceedings of the Workshop
- Pseudo-Hermitian Hamiltonians in Quantum Physics III,
- held in Istanbul, June 2005
- Ed. by M. Znojil
- Czechoslovak Journal of Physics
**55**, 1067 (2005)- "Solvable model of quantum microcanonical states"
- C. M. Bender, D. C. Brody, and D. W. Hook
- Journal of Physics A: Mathematical and General
**38**, L607-L613 (2005) [arXiv: quant-ph/0508004]- "Parity Anomaly in a
**PT**-Symmetric Quartic Hamiltonian"- C. M. Bender
- Plenary talk published in the proceedings of the Workshop
- Pseudo-Hermitian Hamiltonians in Quantum Physics V,
- held in Bologna, July 2006
- Ed. by M. Znojil
- Czechoslovak Journal of Physics
**56**, 1047 (2006)- "Parity Anomaly in a
- "Equivalence of a Complex
**PT**-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly"- C. M. Bender, D. C. Brody, J.-H. Chen, H. F. Jones, K. A. Milton, and M. C. Ogilvie
- Physical Review D
**74**, 025016 (2006) [arXiv: hep-th/0605066]- "Equivalence of a Complex
- "Semiclassical Analysis of a Complex Quartic Hamiltonian"
- C. M. Bender, D. C. Brody, and H. F. Jones
- Physical Review D
**73**, 025002-1 (2006) [arXiv: quant-ph/0509034]- "Entropy and Temperature of a Quantum Carnot Engine"
- C. M. Bender, D. C. Brody, and B. K. Meister
- Published in "The Laws of Thermodynamics--An Anthology of Current Thought as a series of Contemporary Discourse in the Field of Physics"
- Ed. by Jennifer Viegas (Rosen Publishing Company, 2006), pages 21-34
- "
**PT**-Symmetric Versus Hermitian Formulation of Quantum Mechanics"- C. M. Bender, J.-H. Chen, and K. A. Milton
- Journal of Physics A: Mathematical and General
**39**, 1657-1668 (2006) [arXiv: hep-th/0511229]- "
- "Calculation of the Hidden Symmetry Operator for a
**PT**-Symmetric Square Well"- C. M. Bender and B. Tan
- Journal of Physics A: Mathematical and General
**39**, 1945-1953 (2006) [arXiv: quant-ph/0601123]- "Calculation of the Hidden Symmetry Operator for a
- "Classical Trajectories for Complex Hamiltonians"
- C. M. Bender, J.-H. Chen, D. W. Darg, and K. A. Milton
- Journal of Physics A: Mathematical and General
**39**, 4219-4238 (2006) [arXiv: math-ph/0602040]- "Four Easy Pieces"
- C. M. Bender
- Plenary talk published in the proceedings of the Workshop
- Pseudo-Hermitian Hamiltonians in Quantum Physics IV, Stellenbosch, South Africa, November 2005
- Ed. by H. Geyer, D. Heiss, and M. Znojil
- Journal of Physics A: Mathematical and General
**39**, 9993-10012 (2006)- Book review of two books on global warming
- C. M. Bender
- St. Louis Post Dispatch, February 26, 2006, Section F, page F10
- "Faster Than Hermitian Time Evolution"
- C. M. Bender
- SIGMA
**3**(2007), 126, 10 pages [arXiv: hep-th/0712.3910]- Proceedings of the Seventh International Conference in Nonlinear Mathematical Physics
- held in Kyiv, June 2007, Ed. by A. Nikitin
- "
**PT**-Symmetric Quantum Brachistochrone"- C. M. Bender
- In the Proceedings of the of the Ninth Workshop on Non-Perturbative Quantum Chromodynamics
- l'Institut Astrophysique de Paris, June 4-8, 2007
- SLAC eConf lecture series: SLAC econf C0706044
- Edited by B. Mueller, M. A. Rotondo and C.-I Tan
- "
- "Ghost Busting: Making Sense of Non-Hermitian Hamiltonians"
- C. M. Bender
- Plenary talk published in the proceedings of the International Conference
- "Algebraic Analysis of Differential Equations," Kyoto, July, 2005
- Ed. by T. Aoki, H. Majima, Y. Takei, and N. Tose
- RIMS Kokyuroku Symposium Series (Springer, Tokyo, 2007), pp. 55-66
- "Faster than Hermitian Quantum Mechanics"
- C. M. Bender, D. C. Brody, H. F. Jones, and B. K. Meister
- Physical Review Letters
**98**, 040403 (2007) [arXiv: quant-phys/0609032]- "Complex Trajectories of a Simple Pendulum"
- C. M. Bender, D. D. Holm, and D. W. Hook
- Journal of Physics A: Mathematical and Theoretical
**40**, F81-F89 (2007) [arXiv: math-ph/0609068]- "
**PT**-Symmetric Extension of the Korteweg-de Vries Equation"- C. M. Bender, D. C. Brody, J.-H. Chen, and E. Furlan
- Journal of Physics A: Mathematical and Theoretical
**40**, F153-F160 (2007) [arXiv: math-phys/0610003]- "
- "Spontaneous Breaking of Classical
**PT**Symmetry"- C. M. Bender and D. W. Darg
- Journal of Mathematical Physics
**48**, 042703 (2007) [arXiv: hep-th/0703072]- "Spontaneous Breaking of Classical
- "Nonlinear Integral-Equation Formulation of Orthogonal Polynomials"
- C. M. Bender and E. Ben-Naim
- Journal of Physics A: Mathematical and Theoretical
**40**, F9-F15 (2007) [arXiv: math-ph/0610071]- "Making Sense of Non-Hermitian Hamiltonians"
- C. M. Bender
- Invited review article published in Reports on Progress in Physics
**70**, 947-1018 (2007) [arXiv: hep-th/0703096]- "Optimal Shape of a Blob"
- C. M. Bender and M. A. Bender
- Journal of Mathematical Physics
**48**, 073518 (2007) [arXiv: math-ph/0703025]- "Complexified Dynamical Systems"
- C. M. Bender, D. D. Holm, and D. W. Hook
- Journal of Physics A: Mathematical and Theoretical
**40**, F793-F804 (2007) [arXiv: hep-th/0705.3893]- "Nonlinear-Integral-Equation Construction of Orthogonal Polynomials"
- C. M. Bender and E. Ben-Naim
- Journal of Nonlinear Mathematical Physics
**15**73-80 (2008)- Special issue based on the conference "Nonlinear Evolution Equations and
- Dynamical Systems" (NEEDS 2007), held in L'Ametlla de Mar, Spain, June 2007
- "Quantum effects in classical systems having complex energy"
- C. M. Bender, D. C. Brody, and D. W. Hook
- Journal of Physics A: Mathematical and Theoretical
**41**, 352003 (2008) [arXiv: hep-th/0804.4169]- "Does the complex deformation of the Riemann equation exhibit shocks?"
- C. M. Bender and J. Feinberg
- Journal of Physics A: Mathematical and Theoretical
**41**, 244004 (2008) [arXiv: hep-th/0709.2727]- "Interactions of Hermitian and non-Hermitian Hamiltonians"
- C. M. Bender and H. F. Jones
- Journal of Physics A: Mathematical and Theoretical
**41**, 244006 (2008) [arXiv: hep-th/0709.3605]- "Exact Isospectral Pairs of
**PT**-Symmetric Hamiltonians"- C. M. Bender and D. W. Hook
- Journal of Physics A: Mathematical and Theoretical
**41**, 244005 (2008) [arXiv: hep-th/0802.2910]- "Exact Isospectral Pairs of
- "Exactly Solvable
**PT**-Symmetric Hamiltonian Having no Hermitian Counterpart"- C. M. Bender and P. D. Mannheim
- Physical Review D
**78**, 025022 (2008) [arXiv: hep-th/0804.4190]- "Exactly Solvable
- "Conjecture on the Analyticity of
**PT**-Symmetric Potentials"- C. M. Bender, D. W. Hook, and L. R. Mead
- Journal of Physics A: Mathematical and Theoretical
**41**, 392005 (2008) [arXiv: hep-th/0807.0424]- "Conjecture on the Analyticity of
- "Giving Up the Ghost"
- C. M. Bender and P. D. Mannheim
- Journal of Physics A: Mathematical and Theoretical
**41**, 304018 (2008) [arXiv: hep-th/0807.2607]- Special issue based on the 5th International Symposium on Quantum Theory and Symmetries (QTS5)
- held in Vallodolid, Spain, July 2007
- Ed. by M. Gadella, J. M. Izquierdo, S. Kuru, J. Negro, M. del Olmo
- "No-ghost Theorem for the Fourth-Order Derivative Pais-Uhlenbeck Oscillator Model"
- C. M. Bender and P. D. Mannheim
- Physical Review Letters
**100**, 110402 (2008) [arXiv: hep-th/0706.0207]- "Chaotic Systems in Complex Phase Space"
- C. M. Bender, J. Feinberg, D. W. Hook, and D. J. Weir
- Pramana - J. Phys.
**73**(special issue on Non-Hermitian Hamiltonians -- Part II), 453 (2009) [arXiv: hep-th/0809.1975]- "Small-ε behavior of the Non-Hermitian
**PT**-Symmetric Hamiltonian H=p^{2}+x^{2}(ix)^{ε}"- C. M. Bender, K. Besseghir, H. F. Jones, and X. Yin
- Journal of Physics A: Mathematical and Theoretical
**42**, 355301 (2009) [arXiv: hep-th/0906.1291]- "Small-ε behavior of the Non-Hermitian
- "Comment on a recent Brief Report by Shalaby"
- C. M. Bender, G. Benincasa, and H. F. Jones
- Physical Review D
**73**, 128701 (2009) [arXiv: hep-th/0906.4293]- "Optimal Time Evolution for Hermitian and Non-Hermitian Hamiltonians"
- C. M. Bender and D. C. Brody
- Published in
*Time in Quantum Mechanics -- Vol. 2*- Ed. by J. Gonzalo Muga, A. Ruschhaupt, and A. del Campo
- (Springer-Verlag, New York, 2009), ch. 12, 341-360
- "Conduction Bands in Classical Periodic Potentials"
- T. Arpornthip and C. M. Bender
- Pramana - J. Phys.
**73**(special issue on Non-Hermitian Hamiltonians in Quantum Physics -- Part I), 259 (2009)- (arXiv:0905.4694 [math-ph])
- "Compactons in
**PT**-symmetric generalized Korteweg-de Vries Equations"- C. M. Bender, F. Cooper, A. Khare, B. Mihaila, and A. Saxena
- Pramana - J. Phys.
**73**(special issue on Non-Hermitian Hamiltonians in Quantum Physics -- Part I), 375 (2009)- (arXiv:0810.3460v1 [math-ph])
- "Compactons in
- "Nonunique
**C**operator in**PT**Quantum Mechanics"- C. M. Bender and S. P. Klevansky
- Physics Letters A
**373**, 2670-2674 (2009) (arXiv:0905.4673 [hep-th])- "Nonunique
- "Classical Particles Having Complex Energy Exhibit Quantum-Like Behavior"
- C. M. Bender
- In Proceedings of the Tenth Workshop on Non-Perturbative Quantum Chromodynamics
- l'Institut Astrophysique de Paris June 8-12, 2009
- SLAC eConf lecture series: SLAC econf C0906083
- Edited by Berndt Mueller, Mary Ann Rotondo, and Chung-I Tan
- "Families of particles with different masses in
**PT**-symmetric quantum field theory"- C. M. Bender and S. P. Klevansky
- Physical Review Letters
**105**, 031601 (2010) [arXiv: hep-th/1002.3253]- "Families of particles with different masses in
- "Classical Particle in a Complex Elliptic Potential"
- C. M. Bender, D. W. Hook, and K. S. Kooner
- Journal of Physics A: Mathematical and Theoretical
**43**, 165201 (2010) [arXiv: hep-th/1001.1548]- "Almost zero-dimensional
**PT**-symmetric quantum field theories"- C. M. Bender
- In
*Subtleties in Quantum Field Theory*(Lev Lipatov Festschrift)- ed. Dmitri Diakonov, Petersburg Nuclear Physics Institute, Gatchina (2010), pp. 7-16
- [arXiv: hep-th/1003.3881]
- "Almost zero-dimensional
- "
**PT**Symmetry and Necessary and Sufficient Conditions for the Reality of Energy Eigenvalues"- C. M. Bender and P. D. Mannheim
- Physics Letters A
**374**, 1616-1620 (2010) (arXiv:0902.1365 [hep-th])- "
- "Complex Correspondence Principle"
- C. M. Bender, D. W. Hook, P. N. Meisinger, and Q. Wang
- Physical Review Letters
**104**, 061601 (2010) [arXiv: hep-th/0912.2069]- "Probability Density in the Complex Plane"
- C. M. Bender, D. W. Hook, P. N. Meisinger, and Q. Wang
- Annals of Physics
**325**, 2332-2362 (2010) [arXiv: hep-th/0912.4659]- "Steven Alan Orszag" (Obituary)
- C. M. Bender, U. Frisch, K. Sreenivasan, and J. Wettlaufer
- Physics Today
**64**, 66-67 (2011)- "Complex Elliptic Pendulum"
- C. M. Bender, D. W. Hook, and K. S. Kooner
- In
*Asymptotics in Dynamics, Geometry and PDEs; Generalised Borel Summation*, Vol. 1- Edited by O. Costin, F. Fauvet, F. Menous, and D. Sauzin 12
- CRM (Centro di Ricerca Matematica) Series, Ennio De Giorgi
**12**, pp. 1-18, Edizioni della normale (2011)- [arXiv: hep-th/1001.0131]
- "Bound states of
**PT**-symmetric separable potentials"- C. M. Bender and H. F. Jones
- Physical Review A
**84**, 032103 (2011) [arXiv: hep-th/1107.2293]- "Bound states of
- "Quantum counterpart of spontaneously broken
**PT**-symmetry"- C. M. Bender and H. F. Jones
- Journal of Physics A: Mathematical and Theoretical
**44**, 015301 (2011) [arXiv: quant-ph/1008.0782]- "Quantum counterpart of spontaneously broken
- "Quantum tunneling as a classical anomaly"
- C. M. Bender and D. W. Hook
- Journal of Physics A: Mathematical and Theoretical
**44**, 372001 (2011) [arXiv: hep-th/1011.0121]- "Extending
**PT**symmetry from Heisenberg algebra to E2 algebra"- C. M. Bender and R. J. Kalveks
- International Journal of Theoretical Physics
**50**, 955 (2011) [arXiv: hep-th/1009.3236]- "Extending
- "Heuristic explanation of the reality of energy in
**PT**-symmetric quantum field theory"- C. M. Bender
- Proceedings of
*Eleventh Workshop on Non-Perturbative Quantum Chromodynamics*- l'Institut Astrophysique de Paris June 2011
- SLAC econf CR1106064 http://www.slac.stanford.edu/econf/C1106064
- Edited by Berndt Mueller, Mary Ann Rotondo, and Chung-I Tan
- "Heuristic explanation of the reality of energy in
- "Periodic orbits for classical particles having complex energy"
- A. G. Anderson, C. M. Bender, and U. I. Morone
- Physics Letters A
**375**, 3399-3404 (2011) [arXiv: math-ph/1102.4822]- "Response to Shalaby's Comment on `Families of Particles with Different Masses in
**PT**-Symmetric Quantum Field Theory' "- C. M. Bender and S. P. Klevansky
- [arXiv: hep-th/1103.0338]
- "Response to Shalaby's Comment on `Families of Particles with Different Masses in
- "
**PT**-symmetric representations of fermionic algebras"- C. M. Bender and S. P. Klevansky
- Physical Review A
**84**, 024102 (2011) [arXiv: hep-th/1104.4156]- "
- "
**PT**symmetry in relativistic quantum mechanics"- C. M. Bender and P. D. Mannheim
- Physical Review D
**84**, 105038 (2011) [arXiv: hep-th/1107.0501]- "
- "PT-Symmetric Quantum Field Theory"
- C. M. Bender
- in
*Numerical Analysis and Applied Mathematics ICNAAM 2011*- International Conference on Numerical Analysis and Applied Mathematics, Halkidiki, Greece, September 2011
- AIP Conference Proceeding
**1389**, 642-645 (2011)- "Quantum physics with non-Hermitian operators" -- Preface to special issue on non-Hermitian quantum mechanics
- C. M. Bender, A. Fring, U. Gunther, H. Jones
- Journal of Physics A: Mathematical and Theoretical
**45**, 440301 (2012)- "Wentzel-Kramers-Brillouin Analysis of
**PT**-Symmetric Sturm-Liouville Problems"- C. M. Bender and H. F. Jones
- Physical Review A
**85**, 052118 (2012) [arXiv: hep-th/1203.5702]- "Wentzel-Kramers-Brillouin Analysis of
- "Resonances in Extreme Mass-Ratio Inspirals: Asymptotic and Hyperasymptotic Analysis"
- J. Gair, N. Yunes, and C. M. Bender
- Journal of Mathematical Physics
**53**, 032503 (2012) [arXiv: gr-qc/1111.3605]- "Ordinary versus
**PT**-symmetric*φ*quantum field theory"^{3}- C. M. Bender, V. Branchina, and E. Messina
- Physical Review D
**85**, 085001 (2012) [arXiv: hep-th/1201.1244]- "Ordinary versus
- "WKB Analysis of
**PT**-Symmetric Sturm-Liouville Problems"- C. M. Bender and H. F. Jones
- Journal of Physics A: Mathematical and Theoretical
**45**, 444004 (2012) [arXiv: hep-th/1201.1234]- "WKB Analysis of
- "Matrix Representation of the Time Operator"
- C. M. Bender and M. Gianfreda
- Journal of Mathematical Physics
**53**, 062102 (2012) [arXiv: hep-th/1201.3838]- "Asymptotic Analysis of the Boltzmann equation for dark matter relics"
- C. M. Bender and S. Sarkar
- Journal of Mathematical Physics
**53**, 103509 (2012) [arXiv: hep-th/1203.1822]- "
**PT**Phase Transition in Multidimensional Quantum Systems"- C. M. Bender and D. J. Weir
- Journal of Physics A: Mathematical and Theoretical
**45**, 425303 (2012) [arXiv: quant-ph/1206.5100]- "
- "Negative Energy
**PT**-Symmetric Hamiltonians"- C. M. Bender, D. W. Hook, and S. P. Klevansky
- Journal of Physics A: Mathematical and Theoretical
**45**, 444003 (2012) [arXiv: hep-th/1203.6590]- "Negative Energy
- "Unbounded
**C**Symmetries and Their Nonuniqueness"- C. M. Bender and S. Kuzhel
- Journal of Physics A: Mathematical and Theoretical
**45**, 444005 (2012) [arXiv: quant-ph/1207.1176]- "Unbounded
- "Upside-down potentials"
- C. M. Bender
- Journal of Physics: Conference Series
**343**, 012014 (2012)- Proceedings of
*Quantum Theory and Symmetries 7*, Prague, August 2011- "Complex Trajectories in a Classical Periodic Potential"
- A. G. Anderson and C. M. Bender
- Journal of Physics A: Mathematical and Theoretical
**45**, 455101 (2012) [arXiv: hep-th/1205.3330]- "Universal Spectral Behavior of
*x*Potentials"^{2}(ix)^{ε}- C. M. Bender and D. W. Hook
- Physical Review A
**86**, 022113 (2012) [arXiv: hep-th/1205.4425]- "Universal Spectral Behavior of
- "
**PT**Quantum Mechanics -- Recent Results"- C. M. Bender
- AIP Conf. Proc.
**1479**, 517-521 (2012)- "
- "Twofold Transition in
**PT**-Symmetric Coupled Oscillators"- C. M. Bender, M. Gianfreda, B. Peng, S. K. Ozdemir, and L. Yang
- Physical Review A
**88**, 062111 (2013) [arXiv:hep-th/1305.7107]- "Twofold Transition in
- "
**PT**-Symmetric Double-Well Potentials Revisited: Bifurcations, Stability and Dynamics"- A. S. Rodrigues, K. Li, V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and C. M. Bender
- Romanian Reports in Physics
**65**, 5 (2013) [arXiv: nlin/1207.1066]- "
- "
**PT**-symmetric quantum state discrimination"- C. M. Bender, D. C. Brody, J. Caldeira, U. Guenther, B. Meister, and B. Samsonov
- Philosophical Transactions of the Royal Society A
**371**, 20120160 (2013) [arXiv: hep-th/1011.1871]- "
- "Comment on `Numerical estimates of the spectrum for anharmonic PT symmetric potentials' by Bowen
*et al*"- C. M. Bender and S. Boettcher
- Physica Scripta
**87**, 017001 (2013) [arXiv: quant-phys/1210.0426]- "Comment on `Numerical estimates of the spectrum for anharmonic PT symmetric potentials' by Bowen
- "Asymptotic Analysis of the Boltzmann Equation for Dark Matter Relics in the Presence of a Running Dilaton and Space-Time Defects"
- C. M. Bender, N. E. Mavromatos, and S. Sarkar
- Physical Review D
**87**, 055021 (2013) [arXiv: hep-ph/1212.6715]- "PT Quantum Mechanics"
- C. M. Bender, M. DeKieviet, and S. P. Klevansky
- Philosophical Transactions of the Royal Society A
**371**, 20120523 (2013)- "Critical Behavior of the
**PT**-Symmetric*iφ*Quantum Field Theory"^{3}- C. M. Bender, V. Branchina, and E. Messina
- Physical Review D
**87**, 085029 (2013) [arXiv:hep-th/1301.6207]- "Critical Behavior of the
- "Nonuniqueness of the
**C**Operator in**PT**-Symmetric Quantum Mechanics"- C. M. Bender and M. Gianfreda
- Journal of Physics A: Mathematical and Theoretical
**46**, 275306 (2013) [arXiv:hep-th/1302.7047]- "Nonuniqueness of the
- "Observation of
**PT**Phase Transition in a Simple Mechanical System"- C. M. Bender, B. Berntson, D. Parker, and E. Samuel
- American Journal of Physics
**81**, 173 (2013) [arXiv: math-ph/1206.4972]- "Observation of
- "
**PT**-Symmetric Interpretation of Double-Scaling"- C. M. Bender, M. Moshe, and S. Sarkar
- Journal of Physics A: Mathematical and Theoretical
**46**, 102002 (2013) [arXiv: hep-th/1206.4943]- "
- "Double-Scaling Limit of the O(
*N*)-Symmetric Anharmonic Oscillator"- C. M. Bender and S. Sarkar
- Journal of Physics A: Mathematical and Theoretical
**46**, 442001 (2013) [arXiv: hep-th/1307.4348]- "Double-Scaling Limit of the O(
- "Parity-time (
**PT**)-symmetric optical microcavities"- B. Peng, S. K. Ozdemir, S. Fan, F. Nori, M. Gianfreda, C. M. Bender, and L. Yang
- Conference Paper, CLEO: QELS Fundamental Science, San Jose, June 2014
- "Parity-time (
- "Parity-time-symmetric whispering-gallery microcavities"
- B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, L. Yang
- Nature Physics
**10**, 394-398 (2014) [arXiv: 1308.4564]- "Nonlinear Eigenvalue Problems"
- C. M. Bender, A. Fring, and J. Komijani
- Journal of Physics A: Mathematical and Theoretical
**47**, 235204 (2014) [arXiv: math-ph/1401.6161]- "Complex classical motion in potentials with poles and turning points"
- C. M. Bender and D. W. Hook
- Studies in Applied Mathematics
**133**, 318-336 (2014) [arXiv: math-ph/1402.3852]- "Calculation of low-lying energy levels in quantum mechanics"
- C. M. Bender and H. F. Jones
- Journal of Physics A: Mathematical and Theoretical
**47**, 395303 (2014) [arXiv: quant-ph/1402.1158]- "Systems of coupled
**PT**-symmetric oscillators"- C. M. Bender, M. Gianfreda, and S. P. Klevansky
- Physical Review A
**90**, 022114 (2014) [arXiv: math-ph/1406.5967]- "Systems of coupled
- "Loss-induced suppression and revival of lasing"
- B. Peng, S. K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, C. M. Bender, F. Nori, and L. Yang
- Science
**346**, 328-332 (2014) [arXiv: physics.optics/1410.7474]- "Infinite class of
**PT**-symmetric theories from one timelike Liouville Lagrangian"- C. M. Bender, D. W. Hook, N. Mavromatos, and S. Sarkar
- Physical Review Letters
**113**, 231605 (2014) [arXiv: hep-th/1408.2432]- "Infinite class of
- "Non-Hermitian extension of gauge theories and implications for neutrino physics"
- J. Alexandre, C. M. Bender, and P. Millington
- Journal of High Energy Physics
**11**, 111 (2015) [arXiv: hep-th/1508.01203]- "
**PT**-symmetric interpretation of the electromagnetic self-force"- C. M. Bender and M. Gianfreda
- Journal of Physics A: Mathematical and Theoretical
**48**, 34FT01 (2015) [arXiv: hep-th/1409.3828]- "
- "Coupled Oscillator Systems Having Partial
**PT**Symmetry"- A. Beygi, S. P. Klevansky, and C. M. Bender
- Physical Review A
**91**, 062101 (2015) [arXiv: 1503.05725]- "Coupled Oscillator Systems Having Partial
- "Painleve Transcendents and
**PT**-Symmetric Hamiltonians"- C. M. Bender and J. Komijani
- Journal of Physics A: Mathematical and Theoretical
**48**, 475202 (2015) [arXiv: 1502.04089]- "Painleve Transcendents and
- "
**PT**-Symmetric*φ*Theory in d=0 Dimensions"^{4}- C. M. Bender, V. Branchina, and E. Messina
- Submitted [arXiv: 1501.00514]
- "
- "Foldy-Wouthuysen transformation for non-Hermitian Hamiltonians"
- J. Alexandre and C. M. Bender
- Journal of Physics A: Mathematical and Theoretical
**48**, 185403 (2015) [arXiv: 1501.01232]- "
**PT**-symmetric quantum theory"- C. M. Bender
- 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2014)
- Journal of Physics: Conference Series
**631**, 012002 (2015)- [http://iopscience.iop.org/1742-6596/631/1]
- "
- "
**PT**-symmetric interpretation of unstable effective potentials"- C. M. Bender, D. W. Hook, N. E. Mavromatos, and S. Sarkar
- Journal of Physics A: Mathematical and Theoretical
**49**, 45LT01 (2016) [arXiv: hep-th/1506.01970]- "
- "Synthetic versus Dirac monopoles"
- C. M. Bender, M. DeKieviet, and K. A. Milton
- Submitted [arXiv: hep-th/1408.4051]
- "Solitary waves of a
**PT**-symmetric nonlinear Dirac equation"- J. Cuevas-Maraver, P. G. Kevrekidis, A. Saxena, F. Cooper, A. Khare, A. Comech, and C. M. Bender
- Journal of Selected Topics in Quantum Electronics
**22**, 7293090 (2016)- "Solitary waves of a
- "Geometric aspects of space-time reflection symmetry"
- C. M. Bender, D. C. Brody, L. P. Hughston, and B. K. Meister
- Springer Proceedings in Physics
**184**, 185-199 (2016) [arXiv: hep-th/0704.2959]- ed. by F. Bagarello, R. Passante, and C. Trapani
- "Comment on 'On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator' [J. Math. Phys.
**48**, 032701 (2007)] evolution equation"- C. M. Bender, M. Gianfreda, N. Hassanpour, and H. F. Jones
- Journal of Mathematical Physics
**57**, 084101 (2016)- "Comment on 'On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator' [J. Math. Phys.
- Invited feature article "
**PT**symmetry in quantum physics"- C. M. Bender
- Europhysics News
**47/2**, 17 (2016)- Invited feature article "
- Invited article: "Rigorous backbone of
**PT**-symmetric quuntum mechanics"- C. M. Bender
- Journal of Physics A: Mathematical and Theoretical
**49**, 401002 (2016)- Invited article: "Rigorous backbone of
- "Analytic structure of eigenvalues of coupled quantum systems"
- C. M. Bender, A. Felski, N. Hassanpour, and S. P. Klevansky
- Physica Scripta
**91**, 015201 (2017) [arXiv: quant-phys/1702.03839]- "Light neutrino masses from a non-Hermitian Yukawa theory"
- J. Alexandre, C. M. Bender, and P. Millington
- 5th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2016)
- arXiv: 1703.05251
- Journal of Physics: Conference Series
**873**, 012047 (2017)- "
**PT**-symmetric model of immune response"- C. M. Bender, A. Ghatak, and M. Gianfreda
- Journal of Physics A: Mathematical and Theoretical
**50**, 035601 (2017) [arXiv: math-ph/1604.03928]- "
- "Hamiltonian for the zeros of the Riemann zeta function"
- C. M. Bender, D. C. Brody, and M. P. Muller
- Physical Review Letters
**118**, 130201 (2017) [arXiv: quant-phys/1608.03679]- "Nonlinear eigenvalue problems"
- C. M. Bender, J. Komijani, and Q. Wang
- In
*Resurgence, Physics and Numbers*, ed. by F. Fauvet, D. Manchon, S. Marmi, and D. Sauzin- CRM (Centro di Ricerca Matematica) Series, Ennio De Giorgi
**20**, 67-89 (2017)- "Two-dimensional pulse propagation without anomalous dispersion"
- C. M. Bender, F. J. Rodriguez, S. Sarkar, and A. V. Zayats
- Physical Review Letters
**119**, 114301 (2017) [arXiv: cond-mat/1612.08718]- "Behavior of eigenvalues in a region of broken-
**PT**symmetry"- C. M. Bender, N. Hassanpour, D. W. Hook, S. P. Klevansky, C. Sunderhauf, Z. Wen
- Physical Review A
**95**, 052113 (2017) [arXiv: quant-ph/1702.03811]- "Behavior of eigenvalues in a region of broken-
- "Nonlinear eigenvalue problems and
**PT**-symmetric quantum mechanics"- C. M. Bender
- 5th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2016)
- Journal of Physics: Conference Series
**873**, 012002 (2017)- "Nonlinear eigenvalue problems and
- "Scattering off
**PT**-symmetric upside-down potentials"- C. M. Bender and M. Gianfreda
- Physical Review A
**98**, 052118 (2018) [arXiv: quant-phys/1607.06950]- "Scattering off
- "Winding in non-Hermitian systems"
- S. Schindler and C. M. Bender
- J. Phys. A: Math. Theor.
**51**, 055201 (2018) [arXiv: quant-ph/1704.02028]- "Series solutions of
**PT**-symmetric Schroedinger equations"- C. M. Bender, C. Ford, N. Hassanpour, and B. Xia
- Journal of Physics Communications
**2**, 025012 (2018)- "Series solutions of
- "Asymptotic analysis of the local potential approximation to the Wetterich equation"
- C. M. Bender and S. Sarkar
- J. Phys. A: Math. Theor.
**51**, 225202 (2018) [arXiv: hep-th/1801.08106]- "Asymptotic analysis of a pseudo-Hermitian Riemann-zeta Hamiltonian"
- C. M. Bender and D. C. Brody
- J. Phys. A: Math. Theor.
**51**, 135203 (2018)- "Two- and four-dimensional representations of the
**PT**- and**CPT**-symmetric fermionic algebras"- A. Beygi, S. P. Klevansky, and C. M. Bender
- Phys. Rev. A
**97**, 032128 (2018) [arXiv: hep-th/1803.10034]- "Two- and four-dimensional representations of the
- "
**PT**-symmetric quantum field theory in*D*dimensions"- C. M. Bender, N. Hassanpour, S. P. Klevansky, and S. Sarkar
- Physical Review D
**98**, 125003 (2018) [arXiv: hep-th/1810.12479]- "
- "Operator-valued zeta functions and Fourier analysis"
- C. M. Bender and D. C. Brody
- J. Phys. A: Math. Theor.
**52**, 345201 (2019) [arXiv: 1810.01821]- "Nonlinear eigenvalue problems for generalized Painleve equations"
- C. M. Bender, J. Komijani, and Q.-h. Wang
- J. Phys. A: Math. Theor.
**52**, 315202 (2019) [arXiv: 1903.10640]- "Relativistic
**PT**-symmetric fermionic theories in 1+1 and 3+1 dimensions"- A. Beygi, S. P. Klevansky, and C. M. Bender
- Physical Review A
**99**, 062117 (2019) [arXiv: 1904.00878]- "Relativistic
- "Making sense of divergent series for reconstructing a Hamiltonian from its eigenstates and eigenvalues"
- C. M. Bender, D. C. Brody, and M. F. Parry
- American Journal of Physics
**88**, 148 (2020) [arXiv: 1906.03017]- "
**PT**-symmetric quantum field theory"- C. M. Bender
- Invited plenary talk given at DISCRETE 2018, Vienna, November 2018
- J. Phys.: Conf. Ser.
**1586**, 012004 (2020)- "
- "
**PT**-symmetric potentials having continuous spectra"- Z. Wen and C. M. Bender
- J. Phys. A: Math. Theor.
**53**, 375302 (2020) [arXiv: 2002.04398]- "
- "
**PT**-symmetric classical mechanics"- C. M. Bender and D. W. Hook
- J. Phys.: Conf. Series
**2038**, 012003 (2021) [arXiv: 2103.04214]- "
- "Towards perturbative renormalization of
*φ*quantum field theory"^{2}(iφ)^{ε}- A. Felski, C. M. Bender, S. P. Klevansky, and S. Sarkar
- Physical Review D
**104**, 085011 (2021) [arXiv: 2103.07577]- "Towards perturbative renormalization of
- "
**PT**Symmetry and Renormalisation in Quantum Field Theory"- C. M. Bender, A. Felski, S. P. Klevansky, and S. Sarkar
- J. Phys.: Conf. Series
**2038**, 012004 (2021) [arXiv: 2103.14684]- "
- "
**PT**Symmetry"- C. M. Bender
- in
*Time and Science*, Vol. 3- ed. by R. Lestienne and P. Harris (World Scientific, Singapore, 2023)
- "
- "Addendum: Painleve transcendents and
**PT**-symmetric Hamiltonians (2015 J. Phys. A: Math. Theor.**48**475202)"- C. M. Bender and J. Komijani
- J. Phys. A: Math. Theor.
**55**, 109401 (2022) [arXiv: 2107.04935]- "Addendum: Painleve transcendents and
- "Calculation of Green's Functions in
**PT**-Symmetric Quantum Field Theory"- C. M. Bender
- in
*From the Past to the Future -- The Legacy of Lev Lipatov*- ed. by J. Bartels, V. Fadin,E. Levin, A. Levy, V. Kim, and A. Sabio-Vera
- World Scientific, Singapore, 2021
- "Calculation of Green's Functions in
- "Experimentally-realizable
**PT**phase transitions in reflectionless quantum scattering"- M. B. Soley, C. M. Bender, and A. D. Stone
- Physical Review Letters
**130**, 250404 (2023) [arXiv: 2209.05426]- "Experimentally-realizable
- "
**PT**-symmetric*-φ*field theory"^{4}- W.-Y. Ai, C. M. Bender, and S. Sarkar
- Physical Review D
**106**, 125016 (2022) [arXiv: 2209.07897]- "
- "Underdetermined Dyson-Schwinger Equations"
- C. M. Bender, C. Karapoulitidis, and S. P. Klevansky
- Physical Review Letters
**130**, 101602 (2023) [arXiv: 2211.13026]- "New classes of solutions for Euclidean scalar field theories"
- C. M. Bender and S. Sarkar
- Universe
**10**, 10 (2023) [arXiv: 2304.11629]- "Dyson-Schwinger equations in zero dimensions and polynomial approximations"
- C. M. Bender, C. Karapoulitidis, and S. P. Klevansky
- Physical Review D
**108**, 056002 (2023) [arXiv: 2307.01008]- "
**PT**-symmetric quantum mechanics"- C. M. Bender and D. W. Hook
- Invited paper for Reviews of Modern Physics ( submitted 2024) [arXiv: 2312.17386]
- "
- "Complex phases in quantum mechanics"
- C. M. Bender and D. W. Hook
- Invited Perspective paper for Europhysics Letters
**146**, 50001 (2024) [arXiv: 2404.00743]