On the classical-quantum relation of constants of motion

Fabian Belmonte, Tomas Veloz

Research output: Contribution to journalArticle


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.

Original languageEnglish
Article number121
JournalFrontiers in Physics
Issue numberNOV
Publication statusPublished - 13 Nov 2018


  • Angular momenta
  • Constants of motion
  • Diagonalization
  • Example
  • LaTeX
  • Quantization
  • Reduction

ASJC Scopus subject areas

  • Biophysics
  • Materials Science (miscellaneous)
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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