Quasiclassical and Quantum Systems of Angular Momentum. Part II. Quantum Mechanics on Lie Groups and Methods of Group Algebras

Abstract

In Part I of this series we presented the general ideas of applying group-algebraic methods for describing quantum systems. The treatment was there very "ascetic" in that only the structure of a locally compact topological group was used. Below we explicitly make use of the Lie group structure. Basing on differential geometry enables one to introduce explicitly representation of important physical quantities and formulate the general ideas of quasiclassical representation and classical analogy.

References in corpus (3)

• Quantized excitations of internal affine modes and their influence on Raman spectra
• Quasiclassical and Quantum Systems of Angular Momentum. Part I. Group Algebras as a Framework for Quantum-Mechanical Models with Symmetries
• Schrödinger and related equations as Hamiltonian systems, manifolds of second-order tensors and new ideas of nonlinearity in quantum mechanics

Cited by in corpus (2)

• Quasiclassical and Quantum Systems of Angular Momentum. Part III. Group Algebra of $\mathrm{SU}(2)$, Quantum Angular Momentum and Quasiclassical Asymptotics
• Quantized Mechanics of Affinely-Rigid Bodies