Deconstructing non-dissipative non-Dirac-hermitian relativistic quantum systems

TL;DR

This paper introduces a method to construct non-dissipative, non-Dirac-hermitian relativistic quantum systems that are isospectral with traditional Dirac-hermitian systems, using a novel realization of canonical relations and supersymmetry.

Contribution

It presents a new technique to build non-Dirac-hermitian quantum systems that preserve spectra and explores their solvable models through supersymmetry connections.

Findings

Constructed non-Dirac-hermitian systems are isospectral with Dirac-hermitian counterparts.

Provided several exactly solvable models demonstrating the method.

Established a link between the Dirac equation and supersymmetry in this context.

Abstract

A method to construct non-dissipative non-Dirac-hermitian relativistic quantum system that is isospectral with a Dirac-hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving the Dirac matrices and the bosonic degrees of freedom in terms of non-Dirac-hermitian operators, which are hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. Several examples of exactly solvable non-dissipative non-Dirac-hermitian relativistic quantum systems are presented by establishing/employing a connection between Dirac equation and supersymmetry