Bound States of Non-Hermitian Quantum Field Theories

Abstract

The spectrum of the Hermitian Hamiltonian $\frac{1}{2}{p}^2+\frac{1}{2}{m}^2{x}^2+g{x}^4$ ($g>0$), which describes the quantum anharmonic oscillator, is real and positive. The non-Hermitian quantum-mechanical Hamiltonian $H=\frac{1}{2}{p}^2+\frac{1}{2}{m}^2{x}^2-g{x}^4$, where the coupling constant $g$ is real and positive, is $\mathcal{P}\mathcal{T}$-symmetric. As a consequence, the spectrum of $H$ is known to be real and positive as well. Here, it is shown that there is a significant difference between these two theories: When $g$ is sufficiently small, the latter Hamiltonian exhibits a two-particle bound state while the former does not. The bound state persists in the corresponding non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric $-g{\varphi }^4$ quantum field theory for all dimensions $0\le D<3$ but is not present in the conventional Hermitian $g{\varphi }^4$ field theory.

14 pages, 3figures

References in corpus (1)

• Quantum Complex Henon-Heiles Potentials

Cited by in corpus (18)

• Making Sense of Non-Hermitian Hamiltonians
• Must a Hamiltonian be Hermitian?
• Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly
• The C Operator in PT-Symmetric Quantum Theories
• Exact Solution of the Klein-Gordon Equation for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method
• Bound states of the Dirac equation for the PT-symmetric generalized Hulthen potential by the Nikiforov-Uvarov method
• Exponential Type Complex and non-Hermitian Potentials in PT-Symmetric Quantum Mechanics
• Exactly solvable non-Hermitian Jaynes-Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry
• Generalized Swanson models and their solutions
• Two-Point Green's Function in PT-Symmetric Theories
• Nonlinear Non-Hermitian Landau-Zener-Stückelberg-Majorana interferometry
• Kurt Symanzik - a stable fixed point beyond triviality
• Pseudo supersymmetric partners for the generalized Swanson model
• Exact Solutions of the Schrödinger Equation with position-dependent effective mass via general point canonical transformation
• $\mathcal{P}\mathcal{T}$ symmetric models with nonlinear pseudo supersymmetry
• Non-perturbative calculations for the effective potential of the $PT$ symmetric and non-Hermitian $(-g{\varphi }^4)$ field theoretic model
• The Generalized PT-Symmetric Sinh-Gordon Potential Solvable within Quantum Hamilton-Jacobi Formalism
• $T\bar{T}$ deformation on non-Hermitian two coupled SYK model