CPT Groups of Spinor Fields in de Sitter and Anti-de Sitter Spaces

TL;DR

This paper investigates the structure of $CPT$ groups for spinor fields in de Sitter and anti-de Sitter spaces, revealing how their algebraic differences influence $CPT$ symmetries for various particle types.

Contribution

It introduces a novel analysis of $CPT$ groups in curved spacetimes using Clifford algebra automorphisms, highlighting differences between spaces with opposite signatures and particle types.

Findings

$CPT$ groups differ for de Sitter and anti-de Sitter spaces due to algebraic structure.

Distinct $CPT$ groups are identified for neutral and charged particles.

Differences between bosonic and fermionic $CPT$ groups are discussed.

Abstract

$CPT$ groups for spinor fields in de Sitter and anti-de Sitter spaces are defined in the framework of automorphism groups of Clifford algebras. It is shown that de Sitter spaces with mutually opposite signatures correspond to Clifford algebras with different algebraic structure that induces an essential difference of $CPT$ groups associated with these spaces. $CPT$ groups for charged particles are considered with respect to phase factors on the various spinor spaces related with real subalgebras of the simple Clifford algebra over the complex field (Dirac algebra). It is shown that $CPT$ groups for neutral particles which admit particle-antiparticle interchange and $CPT$ groups for truly neutral particles are described within semisimple Clifford algebras with quaternionic and real division rings, respectively. A difference between bosonic and fermionic $CPT$ groups is discussed.