A theory of classical limit for quantum theories which are defined by real Lie algebras

A theory of classical limit is developed for quantum theories, the basic observables of which correspond to elements in some real Lie algebra L0. For both quantum and classical systems based on L0 the basic observables are contained in a unique universal algebra. This is the universal enveloping algebra 𝒰 for the quantum case, and a universal commutative Poisson algebra ℒ for the classical case. 𝒰 and ℒ are connected by a system of contraction maps. For certain sequences of representations and of vector states defined by them renormalized expectation values of the quantum variables are shown to converge to values of the corresponding classical variables at some point in the classical phase space. The classical phase space is obtained as a limit of certain systems of coherent states. The general theory is illustrated by several examples and counterexamples.

Перевод пока недоступен