CARL M. BENDER
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 F1(α)
in Massless Quantum Electrodynamics"
- C. M. Bender and R. W. Keener
- Physical Review D 15, 1572 (1977)
- "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 φ2N Field Theory"
- C. M. Bender and W. E. Caswell
- Journal of Mathematical Physics 19, 2579 (1978)
- "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 gφ4 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)
- "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|α Potential"
- C. M. Bender, L. R. Mead, and L. M. Simmons, Jr.
- Physical Review D 24, 2674 (1981)
- "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 φ4 Field Theory when There is Broken Symmetry"
- C. M. Bender and F. Cooper
- Nuclear Physics B224, 403 (1983)
- "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)
- "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 φ4)4 Field Theory"
- C. M. Bender and
H. F. Jones
- Physical Review D 38, 2526 (1988)
- "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 and F. Cooper
- 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 φ1+14 in Light-Front Field Theory"
- C. M. Bender, S. Pinsky, and B. Van de Sande
- Physical Review D 48, 816 (1993)
- "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)
- "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)
- "Scalar Casimir Effect for a D-Dimensional Sphere"
- C. M. Bender and K. A. Milton
- Physical Review D 50, 6547 (1994)
- "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)
- "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)
- "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)
- "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)
- "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)
- "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, 85001 (2000)
- "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 φ4 Quantum Field Theory"
- C. M. Bender, P. N. Meisinger, and H. Yang
- Physical Review D 63, 45001 (2001)
- "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)
- "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)
- "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)
- "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
- "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]
- "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)
- "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)
- "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)
- "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)
- "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)
- "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]
- "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]
- "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]
- "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]
- "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]
- "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)
- "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]
- "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]
- "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]
- "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]
- "Geometry of PT-Symmetric Quantum Mechanics"
- C. M. Bender,
D. C. Brody, L. P. Hughston, and B. K. Meister [arXiv: hep-th/0704.2959]
- "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]
- "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]
- "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]
- "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]
- "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]
- "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]
- "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
- "Small-ε behavior of the Non-Hermitian PT-Symmetric
Hamiltonian H=p2+x2(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]
- "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])
- "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])
- "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
- "Chaotic Systems in Complex Phase Space"
- C. M. Bender, J. Feinberg,
D. W. Hook, and D. J. Weir
- Pramana - J. Phys. 73 (special issue of Non-Hermitian
Hamiltonians -- Part II), 453 (2009) [arXiv: hep-th/0809.1975]
- "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]
- "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]
- "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]
- "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]
- "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 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]
- "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
- "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]
- "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)
- "PT Quantum Mechanics -- Recent Results"
- C. M. Bender
- AIP Conf. Proc. 1479, 517-521 (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]
- "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 φ3 quantum
field theory"
- C. M. Bender, V. Branchina, and E. Messina
- Physical Review D 85, 085001 (2012) [arXiv: hep-th/1201.1244]
- "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]
- "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]
- "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]
- "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 x2(ix)ε Potentials"
- C. M. Bender and D. W. Hook
- Physical Review A 86, 022113 (2012) [arXiv: hep-th/1205.4425]
- "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]
- "Resolution of Inconsistency in the Double-Scaling Limit"
- C. M. Bender, M. Moshe, and S. Sarkar
- Journal of Physics A: Mathematical and Theoretical 46, 102002 (2013)
[arXiv: hep-th/1206.4943]
- "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]
- "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 (in press, 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 iφ3
Quantum Field Theory"
- C. M. Bender, V. Branchina, and E. Messina
- Physical Review D 87, 085029 (2013) [arXiv:hep-th/1301.6207]
- "Nonuniqueness of the C Operator in PT-Symmetric Quantum
Mechanics"
- C. M. Bender and M. Gianfreda
- Submitted [arXiv:hep-th/1302.7047]