Lorentz violation and Condensed Matter Physics

TL;DR

This paper explores the potential connection between Lorentz violation and phenomena in condensed matter physics, suggesting that Lorentz-violating operators may influence non-relativistic quantum systems.

Contribution

It demonstrates how Lorentz-violating operators can be added to the Dirac equation to derive the Levy-Leblond equation, proposing Lorentz violation's relevance in non-relativistic quantum mechanics.

Findings

Enhanced Lorentz-violating operators lead to Levy-Leblond equation derivation.

Condensed matter phenomena may be influenced by Lorentz violation.

Potential observable effects in non-relativistic quantum systems.

Abstract

We present heuristic arguments that hint to a possible connection of Lorentz violation with observed phenomenon in condensed matter physics. Various references from condensed matter literature are cited where operators in the Standard Model Extension appear to be enhanced. Furthermore, we consider the Levy-Leblond equation, which is the analogue of Dirac equation in non-relativistic quantum mechanics. We show that we can obtain the Levy-Leblond equation by adding enhanced Lorentz violating operators to the Dirac equation. Based on these observations, we propose that Lorentz violation exhibits itself in non-relativistic quantum mechanics.