138 citations · 592 across the 13 of their papers we have counts for
15 papers
Complex phases in quantum mechanics
Carl M. Bender, Daniel W. Hook
Hamilton's equations of motion are local differential equations and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditi…
Foldy-Wouthuysen transformation for non-Hermitian Hamiltonians
Jean Alexandre, Carl M. Bender
Two Non-Hermitian fermion models are proposed and analyzed by using Foldy-Wouthuysen transformations. One model has Lorentz symmetry breaking and the other has a non-Hermitian mass…
Complex classical motion in potentials with poles and turning points
Carl M. Bender, Daniel W. Hook
Complex trajectories for Hamiltonians of the form H=p^n+V(x) are studied. For n=2 time-reversal symmetry prevents trajectories from crossing. However, for n>2 trajectories may inde…
Nonlinear eigenvalue problems
Carl M. Bender, Andreas Fring, Javad Komijani
This paper presents a detailed asymptotic study of the nonlinear differential equation y'(x)=\cos[πxy(x)] subject to the initial condition y(0)=a. Although the differential equatio…
Nonlinear Integral-Equation Formulation of Orthogonal Polynomials
Carl M. Bender, E. Ben-Naim
The nonlinear integral equation P(x)=\int_alpha^beta dy w(y) P(y) P(x+y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomi…
Dual PT-Symmetric Quantum Field Theories
Carl M. Bender, H. F. Jones, R. J. Rivers
Some quantum field theories described by non-Hermitian Hamiltonians are investigated. It is shown that for the case of a free fermion field theory with a mass term the Hamilt…
PT-Symmetric Quantum Electrodynamics
Carl M. Bender, Ines Cavero-Pelaez, Kimball A. Milton +1
The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge is taken to be imaginary. However, if one also specifies that the potent…
Nonperturbative calculation of symmetry breaking in quantum field theory
Carl M. Bender, Kimball A. Milton
A new version of the delta expansion is presented, which, unlike the conventional delta expansion, can be used to do nonperturbative calculations in a self-interacting scalar quant…
Multiple-Scale Analysis of Quantum Systems
Carl M. Bender, Luis M. A. Bettencourt
Conventional weak-coupling Rayleigh-Schrödinger perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multipl…
Multiple-Scale Analysis of the Quantum Anharmonic Oscillator
Carl M. Bender, Luis M. A. Bettencourt
Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation…
Universality in Random Walk Models with Birth and Death
Carl M. Bender, Stefan Boettcher, Peter N. Meisinger
Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers…
Spherically-Symmetric Random Walks in Noninteger Dimension
C. M. Bender, S. Boettcher, M. Moshe
A previous paper (hep-lat/9311011) proposed a new kind of random walk on a spherically-symmetric lattice in arbitrary noninteger dimension . Such a lattice avoids the problems a…
Determination of from the Asymptotic Series for About
C. M. Bender, S. Boettcher
A difficult and long-standing problem in mathematical physics concerns the determination of the value of from the asymptotic series for about . In the p…
Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions
C. M. Bender, A. Duncan, H. F. Jones
Recent proofs of the convergence of the linear delta expansion in zero and in one dimensions have been limited to the analogue of the vacuum generating functional in field theory.…
Spontaneous Symmetry Breaking of phi4(1+1) in Light Front Field Theory
Carl M. Bender, Stephen Pinsky, Brett Van de Sande
We study spontaneous symmetry breaking in phi^4_(1+1) using the light-front formulation of the field theory. Since the physical vacuum is always the same as the perturbative vacuum…