From a quantum theory to a classical one

Abstract

We present and discuss a formal approach for describing the quantum to classical crossover based on the group-theoretic construction of generalized coherent states. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories, and has been recently used for studying open quantum systems whose environment, while becoming macroscopic, may or may not display a classical behaviour. Referring to these recent developments, in this paper we provide the essential elements of Yaffes's approach in the framework of standard quantum mechanics, so as to clarify how the approach can be used without referring to quantum field theory. Moreover, we address the role played by a possible global symmetry in making the large-$N$ limit of the original quantum theory to flow into a formally well defined classical theory, and we specifically consider the quantum-to-classical crossover of angular momentum. We also give details of a paradigmatic example, namely that of $N$ free one-dimensional spinless particles. Finally, we discuss upon the foundational requirement that any classical description should ultimately be derived from an underlying quantum theory, that however is not, and should never be confused with, the one obtained via some quantization procedure of the classical description itself.

arXiv comment13 pages. Accepted for publication in Soft Computing

References in corpus (5)

• Generic emergence of classical features in quantum Darwinism
• Whenever a quantum environment emerges as a classical system, it behaves like a measuring apparatus
• Effective description of the short-time dynamics in open quantum systems
• Parametric description of the quantum measurement process
• Group-Theoretical Derivation of Angular Momentum Eigenvalues in Spaces of Arbitrary Dimensions

Cited by in corpus (5)

• There is only one time
• Threshold size for the emergence of a classical-like behaviour
• A magnetic clock for a harmonic oscillator
• Nature and origin of the operators entering the master equation of an open quantum system
• A formula for the overlap between Generalized Coherent States of any rank one simple Lie algebra