Bound states of non-Hermitian quantum field theories

Abstract

The spectrum of the Hermitian Hamiltonian 12p2+12m2x2+gx4 (g>0), which describes the quantum anharmonic oscillator, is real and positive. The non-Hermitian quantum-mechanical Hamiltonian H=12p2+12m2x2−gx4, where the coupling constant g is real and positive, is PT-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 PT-symmetric −gφ4 quantum field theory for all dimensions 0⩽D<3 but is not present in the conventional Hermitian gφ4 field theory.