Group-theoretical formalism of quantum mechanics and classical-quantum correspondence (Q1201595)

The author presents a mathematical framework for group-theoretical formalism of quantum mechanics and discusses the geometric quantization of the classical systems associated with a Lie group. The classical- quantum correspondence is realized by identifying the quantum observable algebra and its classical analogue with the set of distributions with compact support on a Lie group and on the associated Lie algebra, respectively, both having a convolution-type associative algebraic structure.