### Abstract

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 language | English |
---|---|

Article number | 121 |

Journal | Frontiers in Physics |

Volume | 6 |

Issue number | NOV |

DOIs | |

Publication status | Published - 13 Nov 2018 |

### Fingerprint

### Keywords

- 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

### Cite this

*Frontiers in Physics*,

*6*(NOV), [121]. https://doi.org/10.3389/fphy.2018.00121

}

*Frontiers in Physics*, vol. 6, no. NOV, 121. https://doi.org/10.3389/fphy.2018.00121

**On the classical-quantum relation of constants of motion.** / Belmonte, Fabian; Veloz, Tomas.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the classical-quantum relation of constants of motion

AU - Belmonte, Fabian

AU - Veloz, Tomas

PY - 2018/11/13

Y1 - 2018/11/13

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.

AB - 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.

KW - Angular momenta

KW - Constants of motion

KW - Diagonalization

KW - Example

KW - LaTeX

KW - Quantization

KW - Reduction

UR - http://www.scopus.com/inward/record.url?scp=85058948752&partnerID=8YFLogxK

U2 - 10.3389/fphy.2018.00121

DO - 10.3389/fphy.2018.00121

M3 - Article

AN - SCOPUS:85058948752

VL - 6

JO - Frontiers in Physics

JF - Frontiers in Physics

SN - 2296-424X

IS - NOV

M1 - 121

ER -