TY - JOUR
AU - Belmonte, Fabian
AU - Veloz, Tomas
PY - 2018
M3 - 10.3389/fphy.2018.00121
SP - 121
TI - On the Classical-Quantum Relation of Constants of Motion
JO - Frontiers in Physics
UR - https://www.frontiersin.org/article/10.3389/fphy.2018.00121
VL - 6
SN - 2296-424X
N2 - 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.AMS subject classifications. 68Q25, 68R10, 68U05
ER -