Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation

TL;DR

This paper extends supersymmetric quantum mechanics from non-relativistic to relativistic regimes using Klein-Gordon equations, revealing an 'exceptional-point' instability in ground states due to supersymmetry.

Contribution

It introduces a relativistic supersymmetric quantum mechanics framework based on Klein-Gordon equations, expanding the theoretical understanding of supersymmetry in relativistic quantum systems.

Findings

Supersymmetry leads to 'exceptional-point' instability of ground states.

Framework generalizes non-relativistic supersymmetric quantum mechanics.

Highlights stability issues in relativistic supersymmetric models.

Abstract

Witten's non-relativistic formalism of supersymmetric quantum mechanics was based on a factorization and partnership between Schroedinger equations. We show how it accommodates a transition to the partnership between relativistic Klein-Gordon equations. In such a class of models the requirement of supersymmetry is shown to lead to a certain "exceptional-point" instability of ground states.