CPT groups of higher spin fields

TL;DR

This paper defines and constructs $CPT$ groups for higher spin fields using Clifford algebra automorphisms, providing detailed analysis for spins 1/2, 1, and 3/2, and discussing tensor fields and their particle interpretations.

Contribution

It introduces a general method for constructing $CPT$ groups for any spin and analyzes specific cases, expanding understanding of symmetry groups in higher spin field theories.

Findings

$CPT$ groups are linked to Clifford algebra automorphisms.

Tensor fields correspond to particles with the same spin but different masses.

Explicit $CPT$ groups are derived for spins 1/2, 1, and 3/2.

Abstract

$CPT$ groups of higher spin fields are defined in the framework of automorphism groups of Clifford algebras associated with the complex representations of the proper orthochronous Lorentz group. Higher spin fields are understood as the fields on the Poincar\'{e} group which describe orientable (extended) objects. A general method for construction of $CPT$ groups of the fields of any spin is given. $CPT$ groups of the fields of spin-1/2, spin-1 and spin-3/2 are considered in detail. $CPT$ groups of the fields of tensor type are discussed. It is shown that tensor fields correspond to particles of the same spin with different masses.