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

摘要

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