# Torus as phase space: Weyl quantization, dequantization, and Wigner formalism

## Abstract

The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation for the dynamics of general quantum observables is written through the Moyal brackets on the torus and the support of the Wigner transform is characterized. Finally, a dequantization procedure is introduced that applies, for instance, to the Pauli matrices. As a result we obtain the corresponding classical symbols.

- Authors:

- Dipartimento di Matematica, Università di Bari, I-70125 Bari (Italy)

- Publication Date:

- OSTI Identifier:
- 22596445

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; PAULI SPIN OPERATORS; PHASE SPACE; QUANTIZATION

### Citation Formats

```
Ligabò, Marilena, E-mail: marilena.ligabo@uniba.it.
```*Torus as phase space: Weyl quantization, dequantization, and Wigner formalism*. United States: N. p., 2016.
Web. doi:10.1063/1.4961325.

```
Ligabò, Marilena, E-mail: marilena.ligabo@uniba.it.
```*Torus as phase space: Weyl quantization, dequantization, and Wigner formalism*. United States. doi:10.1063/1.4961325.

```
Ligabò, Marilena, E-mail: marilena.ligabo@uniba.it. Mon .
"Torus as phase space: Weyl quantization, dequantization, and Wigner formalism". United States.
doi:10.1063/1.4961325.
```

```
@article{osti_22596445,
```

title = {Torus as phase space: Weyl quantization, dequantization, and Wigner formalism},

author = {Ligabò, Marilena, E-mail: marilena.ligabo@uniba.it},

abstractNote = {The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation for the dynamics of general quantum observables is written through the Moyal brackets on the torus and the support of the Wigner transform is characterized. Finally, a dequantization procedure is introduced that applies, for instance, to the Pauli matrices. As a result we obtain the corresponding classical symbols.},

doi = {10.1063/1.4961325},

journal = {Journal of Mathematical Physics},

number = 8,

volume = 57,

place = {United States},

year = {Mon Aug 15 00:00:00 EDT 2016},

month = {Mon Aug 15 00:00:00 EDT 2016}

}

DOI: 10.1063/1.4961325

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