CPT theorem in a (5+1) Galilean space-time

TL;DR

This paper extends Galilean space-time to (5+1) dimensions, enabling a covariant definition of parity and demonstrating that the CPT theorem holds in this higher-dimensional Galilean framework.

Contribution

It introduces a (5+1) Galilean space-time framework and proves the CPT theorem within this non-relativistic setting.

Findings

CPT symmetry holds in (5+1) Galilean space-time

Explicit 8x8 gamma matrices are provided for Dirac-type fields

Parity transformation is defined covariantly in the extended space-time

Abstract

We extend the 5-dimensional Galilean space-time to a (5+1) Galilean space-time in order to define a parity transformation in a covariant manner. This allows us to discuss the discrete symmetries in the Galilean space-time, which is embedded in the (5+1) Minkowski space-time. We discuss the Dirac-type field, for which we give the 8\times 8 gamma matrices explicitly. We demonstrate that the CPT theorem holds in the (5+1) Galilean space-time.