# Propagator Dyson-Schwinger equations of Coulomb gauge Yang-Mills theory within the first order formalism

## Abstract

Coulomb gauge Yang-Mills theory within the first order formalism is considered with a view of deriving the propagator Dyson-Schwinger equations. The first order formalism is studied with special emphasis on the Becchi-Rouet-Stora (BRS) invariance and it is found that there exists two forms of invariance--invariance under the standard BRS transform and under a second, nonstandard transform. The field equations of motion and symmetries are derived explicitly and certain exact relations that simplify the formalism are presented. It is shown that the Ward-Takahashi identity arising from invariance under the nonstandard part of the BRS transform is guaranteed by the functional equations of motion. The Feynman rules and the general decomposition of the two-point Green's functions are derived. The propagator Dyson-Schwinger equations are derived and certain aspects (energy independence of ghost Green's functions and the cancellation of energy divergences) are discussed.

- Authors:

- Institut fuer Theoretische Physik, Universitaet Tuebingen, Auf der Morgenstelle 14, D-72076 Tuebingen (Germany)

- Publication Date:

- OSTI Identifier:
- 21011114

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.75.045021; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COULOMB FIELD; EQUATIONS OF MOTION; FIELD EQUATIONS; GREEN FUNCTION; PROPAGATOR; QUANTUM FIELD THEORY; SCHWINGER FUNCTIONAL EQUATIONS; SYMMETRY; YANG-MILLS THEORY

### Citation Formats

```
Watson, P., and Reinhardt, H.
```*Propagator Dyson-Schwinger equations of Coulomb gauge Yang-Mills theory within the first order formalism*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.045021.

```
Watson, P., & Reinhardt, H.
```*Propagator Dyson-Schwinger equations of Coulomb gauge Yang-Mills theory within the first order formalism*. United States. doi:10.1103/PHYSREVD.75.045021.

```
Watson, P., and Reinhardt, H. Thu .
"Propagator Dyson-Schwinger equations of Coulomb gauge Yang-Mills theory within the first order formalism". United States.
doi:10.1103/PHYSREVD.75.045021.
```

```
@article{osti_21011114,
```

title = {Propagator Dyson-Schwinger equations of Coulomb gauge Yang-Mills theory within the first order formalism},

author = {Watson, P. and Reinhardt, H.},

abstractNote = {Coulomb gauge Yang-Mills theory within the first order formalism is considered with a view of deriving the propagator Dyson-Schwinger equations. The first order formalism is studied with special emphasis on the Becchi-Rouet-Stora (BRS) invariance and it is found that there exists two forms of invariance--invariance under the standard BRS transform and under a second, nonstandard transform. The field equations of motion and symmetries are derived explicitly and certain exact relations that simplify the formalism are presented. It is shown that the Ward-Takahashi identity arising from invariance under the nonstandard part of the BRS transform is guaranteed by the functional equations of motion. The Feynman rules and the general decomposition of the two-point Green's functions are derived. The propagator Dyson-Schwinger equations are derived and certain aspects (energy independence of ghost Green's functions and the cancellation of energy divergences) are discussed.},

doi = {10.1103/PHYSREVD.75.045021},

journal = {Physical Review. D, Particles Fields},

number = 4,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}