# Discrete symmetries as automorphisms of the proper Poincare group

## TL;DR

This paper develops a systematic method to identify discrete symmetries within the proper Poincaré group representations, deriving transformation rules for various spin fields without relying on wave equations, and explicitly constructs fields with extended symmetry.

## Contribution

It introduces a novel approach linking involutory automorphisms of the Poincaré group to discrete transformations, enabling direct derivation of transformation rules for arbitrary spin-tensor fields.

## Key findings

- Derived rules for discrete transformations of spin-tensor fields.
- Established correspondence between automorphisms and discrete symmetries.
- Constructed fields with extended Poincaré group representations.

## Abstract

We present the consistent approach to finding the discrete transformations in the representation spaces of the proper Poincar\'e group. To this end we use the possibility to establish a correspondence between involutory automorphisms of the proper Poincar\'e group and the discrete transformations. As a result, we derive rules of the discrete transformations for arbitrary spin-tensor fields without the use of relativistic wave equations. Besides, we construct explicitly fields carrying representations of the extended Poincar\'e group, which includes the discrete transformations as well.