Real spectra for non-Hermitian Dirac equation in 1+1 dimensions with a most general coupling

TL;DR

This paper investigates the 1+1 dimensional non-Hermitian Dirac equation with the most general PT-symmetric couplings, revealing conditions under which real energy spectra can be obtained despite non-Hermiticity.

Contribution

It introduces a comprehensive analysis of the Dirac equation with vector, scalar, and pseudoscalar potentials in a PT-symmetric framework, mapping it to an effective Schrödinger equation.

Findings

Real energy spectra are found despite non-Hermitian potentials.

The Dirac equation with general couplings can be effectively mapped to a PT-symmetric Schrödinger problem.

Conditions for the reality of energies are identified in the PT-symmetric setting.

Abstract

The most general combination of couplings of fermions with external potentials in 1+1 dimensions, must include vector, scalar and pseudoscalar potentials. We consider such a mixing of potentials in a PT-symmetric time-independent Dirac equation. The Dirac equation is mapped into an effective PT-symmetric Schr\"{o}dinger equation. Despite the non-hermiticity of the effective potential, we find real energies for the fermion.