# Confining solution of the Dyson-Schwinger equations in Coulomb gauge

## Abstract

The Dyson-Schwinger equations arising from minimizing the vacuum energy density in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge are solved numerically. A new solution is presented which gives rise to a strictly linearly rising static quark potential and whose existence was previously observed in the infrared analysis of the Dyson-Schwinger equations. For the new solution we also present the static quark potential and calculate the running coupling constant from the ghost-gluon vertex.

- Authors:

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

- Publication Date:

- OSTI Identifier:
- 21011104

- 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.75.045011; (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; COUPLING CONSTANTS; ENERGY DENSITY; GLUONS; HAMILTONIANS; MATHEMATICAL SOLUTIONS; POTENTIALS; QUANTUM FIELD THEORY; QUARKS; SCHWINGER FUNCTIONAL EQUATIONS; YANG-MILLS THEORY

### Citation Formats

```
Epple, D., Reinhardt, H., and Schleifenbaum, W..
```*Confining solution of the Dyson-Schwinger equations in Coulomb gauge*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.045011.

```
Epple, D., Reinhardt, H., & Schleifenbaum, W..
```*Confining solution of the Dyson-Schwinger equations in Coulomb gauge*. United States. doi:10.1103/PHYSREVD.75.045011.

```
Epple, D., Reinhardt, H., and Schleifenbaum, W.. Thu .
"Confining solution of the Dyson-Schwinger equations in Coulomb gauge". United States.
doi:10.1103/PHYSREVD.75.045011.
```

```
@article{osti_21011104,
```

title = {Confining solution of the Dyson-Schwinger equations in Coulomb gauge},

author = {Epple, D. and Reinhardt, H. and Schleifenbaum, W.},

abstractNote = {The Dyson-Schwinger equations arising from minimizing the vacuum energy density in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge are solved numerically. A new solution is presented which gives rise to a strictly linearly rising static quark potential and whose existence was previously observed in the infrared analysis of the Dyson-Schwinger equations. For the new solution we also present the static quark potential and calculate the running coupling constant from the ghost-gluon vertex.},

doi = {10.1103/PHYSREVD.75.045011},

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}

}

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