# Group Theoretical Settling of Spin Zero Relativistic Particle Theories

## TL;DR

This paper develops a group-theoretical framework for spin zero relativistic particles, proposing new irreducible representations of the Poincaré group that differ from the Klein-Gordon theory, aiming to address issues in relativistic quantum theory.

## Contribution

It introduces a novel group-theoretical approach to spin zero particles, identifying four inequivalent theories based on new Poincaré group representations, bypassing canonical quantization.

## Key findings

- Four distinct theories for spin 0 particles are fully characterized.
- These theories differ fundamentally from Klein-Gordon theory.
- The approach avoids traditional difficulties in relativistic quantum mechanics.

## Abstract

In order to avoid the difficulties encountered by relativistic quantum theory of single particles, we pursue a deductive development of the theory from physical principles, without canonical quantization, by making use of group-theoretical methods. Our work has pointed out the necessity of new classes of irreducible representations of the Poincar\'e group the quantum theory of a particle can be based on. For spin 0 particle, four inequivalent theories are completely determined, with fundamental differences with respect to Klein-Gordon theory.