CPT groups for spinor field in de Sitter space

TL;DR

This paper investigates the structure of CPT symmetry groups for spinor fields in de Sitter space, revealing two isomorphic groups derived from wave equations and algebraic automorphisms.

Contribution

It introduces two distinct CPT groups for spinor fields in de Sitter space and proves their isomorphism, connecting physical and algebraic perspectives.

Findings

Two CPT groups are constructed for spinor fields in de Sitter space.

Both groups are shown to be isomorphic.

The groups are derived from wave equations and algebraic automorphisms.

Abstract

A group structure of the discrete transformations (parity, time reversal and charge conjugation) for spinor field in de Sitter space are studied in terms of extraspecial finite groups. Two $CPT$ groups are introduced, the first group from an analysis of the de Sitter-Dirac wave equation for spinor field, and the second group from a purely algebraic approach based on the automorphism set of Clifford algebras. It is shown that both groups are isomorphic to each other.