Schr\"odinger-Pauli Equation for the Standard Model Extension CPT-Violating Dirac Equation

TL;DR

This paper derives a non-relativistic Schr"odinger-Pauli-like equation from the CPT-violating Dirac equation in the Standard Model Extension, focusing on minimal electromagnetic coupling and specific CPT-violating terms.

Contribution

It provides a simplified non-relativistic limit of the SME CPT-violating Dirac equation considering only certain CPT-violating terms and first-order momentum effects.

Findings

Derivation of a Schr"odinger-Pauli-like equation for SME CPT violation.

Analysis of toy systems illustrating the effects of CPT-violating terms.

Comparison with previous free particle treatments by Kostelecky and Lane.

Abstract

It is instructive to investigate the non-relativistic limit of the simplest Standard Model Extension (SME) CPT-violating Dirac-like equation but with minimal coupling to the electromagnetic fields. In this limit, it becomes an intuitive Schr\"odinger-Pauli-like equation. This is comparable to the free particle treatment as explored by Kostelecky and Lane, but this exercise only considers the $a$ and $b$ CPT-violating terms and $\vec{p}/m$ terms to first order. Several toy systems are discussed.