The CPT group of the spin-3/2 field

TL;DR

This paper determines the structure of the CPT symmetry groups for the spin-3/2 field, revealing they are isomorphic to known groups, similar to the Dirac field, despite no initial expectation of this coincidence.

Contribution

It explicitly identifies the matrix and operator CPT groups for the spin-3/2 field and shows they are isomorphic to specific well-known groups, extending understanding of CPT symmetries.

Findings

CPT groups for spin-3/2 field are isomorphic to D4⋊Z2 and Q×Z2.

These groups are identical to those of the Dirac field.

The result is unexpected given the different nature of the fields.

Abstract

We find out that both the matrix and the operator CPT groups of the spin-3/2 field (with or without mass) are respectively isomorphic to $D_4\rtimes\mathbb{Z}_2$ and $Q\times\mathbb{Z}_2$. These groups are exactly the same groups as for the Dirac field, though there is no a priori reason why they should coincide.