Quasiclassical and Quantum Systems of Angular Momentum. Part III. Group Algebra of ${\rm SU}(2)$, Quantum Angular Momentum and Quasiclassical Asymptotics

TL;DR

This paper explores the group algebra of SU(2), focusing on quantum angular momentum and quasiclassical asymptotics, advancing the mathematical framework for angular momentum in quantum systems.

Contribution

It provides a detailed SU(2)-specific analysis of group algebras and their application to quantum angular momentum and quasiclassical limits.

Findings

SU(2) group algebra formulation for angular momentum

Quasiclassical asymptotic methods developed for SU(2)

Application to quantum angular momentum problems

Abstract

This is the third part of our series "Quasiclassical and Quantum Systems of Angular Momentum". In two previous parts we have discussed the methods of group algebras in formulation of quantum mechanics and certain quasiclassical problems. Below we specify to the special case of the group ${\rm SU}(2)$ and its quotient ${\rm SO}(3,\mathbb{R})$, and discuss just our main subject in this series, i.e., angular momentum problems. To be more precise, this is the purely ${\rm SU}(2)$-treatment, so formally this might also apply to isospin. However. it is rather hard to imagine realistic quasiclassical isospin problems.