# BRST quantization and coadjoint orbit theories

## Abstract

A new harmonic'' Becchi-Rouet-Stora-Tyutin method is presented for quantizing those dynamical systems having second-class constraints which split into holomorphic and antiholomorphic algebras. These theories include those whose phase spaces are coadjoint orbits of a compact semisimple Lie group. The method also applies to theories with holomorphic first-class constraints which have nonvanishing brackets with their antiholomorphic conjugates. An operatorial quantization, resembling supersymmetric quantum mechanics, is presented. In addition, a general path integral is given and is shown to reduce to that given by Batalin, Fradkin, and Vilkovisky.

- Authors:

- (Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (US))

- Publication Date:

- OSTI Identifier:
- 5794433

- DOE Contract Number:
- FG02-85ER40231

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review, D (Particles Fields); (USA); Journal Volume: 43:10

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QUANTUM MECHANICS; SUPERSYMMETRY; HAMILTONIANS; HARMONICS; HILBERT SPACE; MATRIX ELEMENTS; PHASE SPACE; QUANTIZATION; BANACH SPACE; MATHEMATICAL OPERATORS; MATHEMATICAL SPACE; MECHANICS; OSCILLATIONS; QUANTUM OPERATORS; SPACE; SYMMETRY; 645300* - High Energy Physics- Particle Invariance Principles & Symmetries; 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics

### Citation Formats

```
Allen, T.J..
```*BRST quantization and coadjoint orbit theories*. United States: N. p., 1991.
Web. doi:10.1103/PhysRevD.43.3442.

```
Allen, T.J..
```*BRST quantization and coadjoint orbit theories*. United States. doi:10.1103/PhysRevD.43.3442.

```
Allen, T.J.. Wed .
"BRST quantization and coadjoint orbit theories". United States.
doi:10.1103/PhysRevD.43.3442.
```

```
@article{osti_5794433,
```

title = {BRST quantization and coadjoint orbit theories},

author = {Allen, T.J.},

abstractNote = {A new harmonic'' Becchi-Rouet-Stora-Tyutin method is presented for quantizing those dynamical systems having second-class constraints which split into holomorphic and antiholomorphic algebras. These theories include those whose phase spaces are coadjoint orbits of a compact semisimple Lie group. The method also applies to theories with holomorphic first-class constraints which have nonvanishing brackets with their antiholomorphic conjugates. An operatorial quantization, resembling supersymmetric quantum mechanics, is presented. In addition, a general path integral is given and is shown to reduce to that given by Batalin, Fradkin, and Vilkovisky.},

doi = {10.1103/PhysRevD.43.3442},

journal = {Physical Review, D (Particles Fields); (USA)},

number = ,

volume = 43:10,

place = {United States},

year = {Wed May 15 00:00:00 EDT 1991},

month = {Wed May 15 00:00:00 EDT 1991}

}

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