# New representations of Poincar\'e group for consistent Relativistic Particle Theories

## TL;DR

This paper extends the class of irreducible Poincaré group representations, enabling the development of consistent relativistic particle theories, including new particle species and improved formulations for Klein-Gordon particles.

## Contribution

It explicitly determines an extended class of irreducible Poincaré group representations with positive mass, previously excluded, facilitating new relativistic particle theories.

## Key findings

- New representations lead to consistent Klein-Gordon particle theories
- Extended class includes previously missed irreducible representations
- Enables formulation of new particle species

## Abstract

Though the irreducible representations of the Poincare' group form the groundwork for the formulation of relativistic quantum theories of a particle, robust classes of such representations are missed in current formulations of these theories. In this work the extended class of irreducible representations with positive `mass' parameter is explicitly determined. Several new representations in such extension, so far excluded, give rise to consistent theories for Klein-Gordon particles and also to new species of particle theories.