Isospectral Local Hamiltonians for Perturbative PT-symmetric Hamiltonians

Abstract

A new method to work out the Hermitian correspondence of a PT-symmetric quantum mechanical Hamiltonian is proposed. In contrast to the conventional method, the new method ends with a local Hamiltonian of the form p^2/2+m^2x^2/2+v(x) without any higher-derivative terms. This method is demonstrated in the perturbative regime. Possible extensions to multi-variable quantum mechanics and quantum field theories are discussed.