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 Yaffe (Rev Mod Phys 54:407, 1982) 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 (Liuzzo-Scorpo et al. in EPL (Europhys Lett) 111(4):40008, 2015; Rossi et al. in Phys Rev A 96:032116, 2017; Foti et al. in Quantum 3:179, 2019; Coppo in Schwarzschild black holes as macroscopic quantum systems, Università degli studi di Firenze, Florence, 2019). Referring to these recent developments, in this paper we provide the essential elements of Yaffe’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.

我们提出并讨论一种基于广义相干态的群理论构造描述量子到经典交叉的形式方法。该方法最初由Yaffe（Rev Mod Phys 54：407，1982）于1982年提出，用于解决大氮量子场理论，最近已用于研究开放量子系统，其环境虽然变得宏观，但可能会或可能不会表现出经典行为（Liuzzo-Scorpo等人，EPL（Europhys Lett）111（4）：40008，2015； Rossi等人在Phys Rev A 96：032116，2017; Foti等人在Quantum 3：179，2019; Coppo在Schwarzschild黑洞中作为宏观量子系统，佛罗伦萨大学，佛罗伦萨，2019）。参照这些最新发展，本文在标准量子力学的框架内提供了Yaffe方法的基本要素，以阐明如何在不参考量子场论的情况下使用该方法。此外，我们可以讨论使得large-可能由一个全球性的对称性发挥的作用ñ原始量子理论的局限性流入形式上明确定义的经典理论，因此我们专门考虑角动量的量子与经典的交叉。我们还给出了一个范例示例的细节，即N个自由的一维无纺粒子。最后，我们讨论了一个基本要求，即任何经典描述都应最终从一种基本的量子理论中衍生而来，但是，该古典理论不应，也不应与通过经典描述本身的某种量化程序获得的描述相混淆。