The CPT Group in the de Sitter Space

TL;DR

This paper investigates the discrete symmetries of the Dirac field in de Sitter space, revealing the finite group structure of CPT transformations and their isomorphism with Minkowski space counterparts.

Contribution

It introduces a group-theoretic analysis of $P$, $T$, $C$ transformations in de Sitter space using Clifford algebras, establishing their finite group structure and isomorphism with Minkowski space.

Findings

CPT groups in de Sitter space are finite and well-defined.

The CPT group in de Sitter space is isomorphic to that in Minkowski space.

Discrete transformations form an automorphism set of Clifford algebras.

Abstract

$P$-, $T$-, $C$-transformations of the Dirac field in the de Sitter space are studied in the framework of an automorphism set of Clifford algebras. Finite group structure of the discrete transformations is elucidated. It is shown that $CPT$ groups of the Dirac field in Minkowski and de Sitter spaces are isomorphic.