N=1 Supersymetric Quantum Mechanics in a Scenario with Lorentz-Symmetry Violation

TL;DR

This paper demonstrates that a non-relativistic particle with spin, interacting with electromagnetic fields and a Lorentz-violating background, exhibits an inherent N=1 supersymmetry when described using a superspace framework.

Contribution

It introduces a superspace formulation showing supersymmetry in a Lorentz-violating scenario for particles with spin.

Findings

Supersymmetry emerges naturally in the described system.

The superspace approach unifies particle and spin degrees of freedom.

Lorentz symmetry breaking does not prevent supersymmetry from appearing.

Abstract

We show in this paper that the dynamics of a non-relativistic particle with spin, coupled to an external electromagnetic field and to a background that breaks Lorentz symmetry, is naturally endowed with an N=1-supersymmetry. This result is achieved in a superspace approach where the particle coordinates and the spin degrees of freedom are components of the same supermultiplet.