Irreducible representations of the CPT groups in QED

TL;DR

This paper constructs the irreducible representations of CPT groups for the Dirac field and electromagnetic potential in QED, providing a comprehensive mathematical framework for both free and interacting fields.

Contribution

It introduces the first detailed construction of the inequivalent irreducible representations of CPT groups for key quantum fields in QED, including the Dirac equation.

Findings

Irreducible representations of CPT groups for Dirac and electromagnetic fields are explicitly constructed.

Results apply to both free and interacting quantum electrodynamics fields.

Provides a complete mathematical classification of CPT group representations in QED.

Abstract

We construct the inequivalent irreducible representations (IIR's) of the CPT groups of the Dirac field operator \hat{\psi} and the electromagnetic quantum potential \hat{A}_\mu. The results are valid both for free and interacting (QED) fields. Also, and for the sake of completeness, we construct the IIR's of the CPT group of the Dirac equation.