# Automorphisms in Gauge Theories and the Definition of CP and P

## TL;DR

This paper explores how CP and parity symmetries can be defined in general gauge theories through automorphisms of the gauge Lie algebra, with focus on scalar interactions and Yukawa couplings.

## Contribution

It provides a framework linking discrete symmetries to gauge algebra automorphisms, clarifying their definitions in complex gauge theories.

## Key findings

- Automorphisms of gauge Lie algebra can define CP and P symmetries.
- Conditions for CP invariance of Yukawa couplings are identified.
- Implications for scalar gauge interactions are discussed.

## Abstract

We study the possibilities to define CP and parity in general gauge theories by utilizing the intimate connection of these discrete symmetries with the group of automorphisms of the gauge Lie algebra. Special emphasis is put on the scalar gauge interactions and the CP invariance of the Yukawa couplings.