# Harmonic BRST quantization of systems with irreducible holomorphic bosonic and fermionic constraints

## Abstract

We consider systems with second-class constraints or, equivalently, first-class holomorphic constraints. We show that the harmonic Becchi-Rouet-Stora-Tyutin method of quantizing systems with bosonic holomorphic constraints extends to systems having both bosonic and fermionic holomorphic constraints. The ghosts for bosonic holomorphic constraints in the harmonic BRST method have a Poisson brackets structure different from that of the ghosts in the usual BRST method, which applies to systems with real first-class constraints. Apart from this exotic ghost structure for bosonic constraints, the new feature of the harmonic BRST method is the introduction of two new holomorphic BRST charges [Theta] and [bar [Theta]] and the addition of an extra term [minus][beta][l brace][Theta],[bar [Theta]][r brace] to the BRST-invariant Hamiltonian. We apply the Fradkin-Vilkovisky theorem to general systems with mixed bosonic and fermionic holomorphic constraints and show that, taking an appropriate limit, the extra term in the harmonic BRST-modified path integral reproduces the correct Senjanovic measure.

- Authors:

- (Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706 (United States))

- Publication Date:

- OSTI Identifier:
- 6498451

- DOE Contract Number:
- AC02-76ER00881

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review, D (Particles Fields); (United States); Journal Volume: 47:12

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOSONS; QUANTIZATION; FERMIONS; CONSTRAINTS; DUALITY; HAMILTONIANS; HILBERT SPACE; MATRICES; SPIN; ANGULAR MOMENTUM; BANACH SPACE; MATHEMATICAL OPERATORS; MATHEMATICAL SPACE; PARTICLE PROPERTIES; QUANTUM OPERATORS; SPACE; 662340* - Hadron Interactions- (1992-)

### Citation Formats

```
Allen, T.J., and Crossley, D.B..
```*Harmonic BRST quantization of systems with irreducible holomorphic bosonic and fermionic constraints*. United States: N. p., 1993.
Web. doi:10.1103/PhysRevD.47.5494.

```
Allen, T.J., & Crossley, D.B..
```*Harmonic BRST quantization of systems with irreducible holomorphic bosonic and fermionic constraints*. United States. doi:10.1103/PhysRevD.47.5494.

```
Allen, T.J., and Crossley, D.B.. Tue .
"Harmonic BRST quantization of systems with irreducible holomorphic bosonic and fermionic constraints". United States.
doi:10.1103/PhysRevD.47.5494.
```

```
@article{osti_6498451,
```

title = {Harmonic BRST quantization of systems with irreducible holomorphic bosonic and fermionic constraints},

author = {Allen, T.J. and Crossley, D.B.},

abstractNote = {We consider systems with second-class constraints or, equivalently, first-class holomorphic constraints. We show that the harmonic Becchi-Rouet-Stora-Tyutin method of quantizing systems with bosonic holomorphic constraints extends to systems having both bosonic and fermionic holomorphic constraints. The ghosts for bosonic holomorphic constraints in the harmonic BRST method have a Poisson brackets structure different from that of the ghosts in the usual BRST method, which applies to systems with real first-class constraints. Apart from this exotic ghost structure for bosonic constraints, the new feature of the harmonic BRST method is the introduction of two new holomorphic BRST charges [Theta] and [bar [Theta]] and the addition of an extra term [minus][beta][l brace][Theta],[bar [Theta]][r brace] to the BRST-invariant Hamiltonian. We apply the Fradkin-Vilkovisky theorem to general systems with mixed bosonic and fermionic holomorphic constraints and show that, taking an appropriate limit, the extra term in the harmonic BRST-modified path integral reproduces the correct Senjanovic measure.},

doi = {10.1103/PhysRevD.47.5494},

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

number = ,

volume = 47:12,

place = {United States},

year = {Tue Jun 15 00:00:00 EDT 1993},

month = {Tue Jun 15 00:00:00 EDT 1993}

}