### Abstract

We consider a local, renormalizable, BRST-invariant action for QCD in Coulomb gauge that contains auxiliary bose and fermi ghost fields. It possess a non-perturbative vacuum that spontaneously breaks BRST-invariance. The vacuum condition leads to a gap equation that introduces a mass scale. Calculations are done to one-loop order in a perturbative expansion about this vacuum. They are free of the finite-T infrared divergences found by Lindé and which occur in the order g
^{6} corrections to the Stefan-Boltzmann equation of state. We obtain a finite result for these corrections. Renormalization and renormalization-group flow are described. We calculate the ghost propagator and color-Coulomb potential to one-loop and find that they are long range, whereas the 3-dimensionally transverse would-be physical gluon propagator is suppressed like k
^{2} at small |k|. These one-loop results accord with the Gribov scenario in Coulomb gauge and with recent numerical determinations of these quantities. When the auxiliary fields are integrated out, one obtains the standard Coulomb gauge action with a cut-off at the Gribov horizon.

Original language | English (US) |
---|---|

Pages (from-to) | 127-143 |

Number of pages | 17 |

Journal | Brazilian Journal of Physics |

Volume | 37 |

Issue number | 1 B |

State | Published - Mar 2007 |

### Fingerprint

### Keywords

- Gluon plasma
- QCD
- Spontaneous breaking of BRST

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Brazilian Journal of Physics*,

*37*(1 B), 127-143.

**Equation of state of gluon plasma and renormalization of local action.** / Zwanziger, Daniel.

Research output: Contribution to journal › Article

*Brazilian Journal of Physics*, vol. 37, no. 1 B, pp. 127-143.

}

TY - JOUR

T1 - Equation of state of gluon plasma and renormalization of local action

AU - Zwanziger, Daniel

PY - 2007/3

Y1 - 2007/3

N2 - We consider a local, renormalizable, BRST-invariant action for QCD in Coulomb gauge that contains auxiliary bose and fermi ghost fields. It possess a non-perturbative vacuum that spontaneously breaks BRST-invariance. The vacuum condition leads to a gap equation that introduces a mass scale. Calculations are done to one-loop order in a perturbative expansion about this vacuum. They are free of the finite-T infrared divergences found by Lindé and which occur in the order g 6 corrections to the Stefan-Boltzmann equation of state. We obtain a finite result for these corrections. Renormalization and renormalization-group flow are described. We calculate the ghost propagator and color-Coulomb potential to one-loop and find that they are long range, whereas the 3-dimensionally transverse would-be physical gluon propagator is suppressed like k 2 at small |k|. These one-loop results accord with the Gribov scenario in Coulomb gauge and with recent numerical determinations of these quantities. When the auxiliary fields are integrated out, one obtains the standard Coulomb gauge action with a cut-off at the Gribov horizon.

AB - We consider a local, renormalizable, BRST-invariant action for QCD in Coulomb gauge that contains auxiliary bose and fermi ghost fields. It possess a non-perturbative vacuum that spontaneously breaks BRST-invariance. The vacuum condition leads to a gap equation that introduces a mass scale. Calculations are done to one-loop order in a perturbative expansion about this vacuum. They are free of the finite-T infrared divergences found by Lindé and which occur in the order g 6 corrections to the Stefan-Boltzmann equation of state. We obtain a finite result for these corrections. Renormalization and renormalization-group flow are described. We calculate the ghost propagator and color-Coulomb potential to one-loop and find that they are long range, whereas the 3-dimensionally transverse would-be physical gluon propagator is suppressed like k 2 at small |k|. These one-loop results accord with the Gribov scenario in Coulomb gauge and with recent numerical determinations of these quantities. When the auxiliary fields are integrated out, one obtains the standard Coulomb gauge action with a cut-off at the Gribov horizon.

KW - Gluon plasma

KW - QCD

KW - Spontaneous breaking of BRST

UR - http://www.scopus.com/inward/record.url?scp=34249021163&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249021163&partnerID=8YFLogxK

M3 - Article

VL - 37

SP - 127

EP - 143

JO - Brazilian Journal of Physics

JF - Brazilian Journal of Physics

SN - 0103-9733

IS - 1 B

ER -