On the Classical-Quantum Relation of Constants of Motion

Frontiers in Physics

Belmonte, Fabian¹  Veloz, Tomas³ 

[1] Department of Mathematics, Universidad CatóInstitute of Philosophy and Complexity Sciences, Chile;lica del Norte, Chile

关键词: Weyl calculus;    constants of motion;    quantization;    Classical quantum correspondence;    angular momenta;   

DOI  :  10.3389/fphy.2018.00121

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

Groenewold-Van Hove theorem suggest that is not always possible to transform classical observables into quantum observables (a process known as quantization) in a way that, for all Hamiltonians, the constants of motion are preserved. The latter is a strong shortcoming for the ultimate goal of quantization, as one would expect that the notion of ``constants of motion" is independent of the chosen physical scheme. It has been recently developed an approach to quantization that instead of mapping every classical observable into a quantum observable, it focuses on mapping the constants of motion themselves. In this article we will discuss the relations between classical and quantum theory under the light of this new form of quantization. In particular, we will examine the mapping of a class of operators that generalizes angular momentum where quantization satisfies the usual desirable properties.

【 授权许可】

CC BY