Foldy-Wouthuysen transformation for non-Hermitian Hamiltonians

TL;DR

This paper applies the Foldy-Wouthuysen transformation to two non-Hermitian fermion models, revealing conditions under which they have real energies and conserved currents despite non-Hermiticity.

Contribution

It introduces two non-Hermitian fermion models analyzed via Foldy-Wouthuysen transformation, highlighting their real spectra and conserved currents in specific parameter regions.

Findings

Models exhibit real energies in certain parameter regimes

Locally conserved currents are identified in these models

Analysis demonstrates the applicability of Foldy-Wouthuysen transformation to non-Hermitian systems

Abstract

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 term. It is shown that each model has real energies in a given region of parameter space, where they have a locally conserved current.