Classification of quantum relativistic orientable objects

TL;DR

This paper develops a comprehensive group-theoretical classification scheme for orientable relativistic quantum objects in 3+1 dimensions, extending previous work to include internal symmetries and offering insights into elementary spinning particles.

Contribution

It introduces a classification method based on maximal commuting operators on the Poincare group, incorporating internal symmetries for a more complete understanding of relativistic quantum objects.

Findings

Reproduces the usual classification of spinning particles

Provides a group-theoretical interpretation of phenomenological classifications

Extends classification to include internal symmetries

Abstract

Started from our work "Fields on the Poincare Group and Quantum Description of Orientable Objects" (EPJC,2009), we consider here a classification of orientable relativistic quantum objects in 3+1 dimensions. In such a classification, one uses a maximal set of 10 commuting operators (generators of left and right transformations) in the space of functions on the Poincare group. In addition to usual 6 quantum numbers related to external symmetries (given by left generators), there appear additional quantum numbers related to internal symmetries (given by right generators). We believe that the proposed approach can be useful for description of elementary spinning particles considering as orientable objects. In particular, their classification in the framework of the approach under consideration reproduces the usual classification but is more comprehensive. This allows one to give a group-theoretical interpretation to some facts of the existing phenomenological classification of known spinning particles.