# Phase-space quantization of field theory.

## Abstract

In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab., IL (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 11761

- Report Number(s):
- ANL-HEP-CP-99-06

TRN: US0102107

- DOE Contract Number:
- W-31109-ENG-38

- Resource Type:
- Conference

- Resource Relation:
- Conference: Workshop on Gauge Theory and Integrable Models, Kyoto (JP), 01/26/1999--01/29/1999; Other Information: PBD: 20 Apr 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CANONICAL TRANSFORMATIONS; WIGNER DISTRIBUTION; DISTRIBUTION FUNCTIONS; GAUGE INVARIANCE; HARMONIC OSCILLATORS; PHASE SPACE; QUANTIZATION; SCALAR FIELDS

### Citation Formats

```
Curtright, T., and Zachos, C..
```*Phase-space quantization of field theory.*. United States: N. p., 1999.
Web.

```
Curtright, T., & Zachos, C..
```*Phase-space quantization of field theory.*. United States.

```
Curtright, T., and Zachos, C.. Tue .
"Phase-space quantization of field theory.". United States. https://www.osti.gov/servlets/purl/11761.
```

```
@article{osti_11761,
```

title = {Phase-space quantization of field theory.},

author = {Curtright, T. and Zachos, C.},

abstractNote = {In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Apr 20 00:00:00 EDT 1999},

month = {Tue Apr 20 00:00:00 EDT 1999}

}

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