### Abstract

The thermodynamic limit of lattice gauge theory is derived in a gauge which is optimized to make all link variables as close to unity as possible. The derivation rests upon (1) a precise bound on the fundamental modular region and (2) a direct evaluation of the functional integral of the Wilson lattice by the saddle-point method that is valid in the thermodynamic limit. The result confirms the calculational scheme obtained previously, which differs from the Faddeev-Popov scheme by the incorporation of non-perturbative effects, but which remains perturbatively renormalizable. The lattce Faddeev-Popov propagator, which appears in the modified action, acquires a dipole singularity at zero momentum, characteristic of long-range correlations. This is sufficient to produce an area law for Wilson loops, provided that unevaluated terms to not cancel the effect found.

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

Pages (from-to) | 198-200 |

Number of pages | 3 |

Journal | Nuclear Physics B - Proceedings Supplements |

Volume | 34 |

Issue number | C |

DOIs | |

State | Published - 1994 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Fundamental modular region, Boltzmann factor, and area law in Lattice gauge theory.** / Zwanziger, Daniel.

Research output: Contribution to journal › Article

*Nuclear Physics B - Proceedings Supplements*, vol. 34, no. C, pp. 198-200. https://doi.org/10.1016/0920-5632(94)90343-3

}

TY - JOUR

T1 - Fundamental modular region, Boltzmann factor, and area law in Lattice gauge theory

AU - Zwanziger, Daniel

PY - 1994

Y1 - 1994

N2 - The thermodynamic limit of lattice gauge theory is derived in a gauge which is optimized to make all link variables as close to unity as possible. The derivation rests upon (1) a precise bound on the fundamental modular region and (2) a direct evaluation of the functional integral of the Wilson lattice by the saddle-point method that is valid in the thermodynamic limit. The result confirms the calculational scheme obtained previously, which differs from the Faddeev-Popov scheme by the incorporation of non-perturbative effects, but which remains perturbatively renormalizable. The lattce Faddeev-Popov propagator, which appears in the modified action, acquires a dipole singularity at zero momentum, characteristic of long-range correlations. This is sufficient to produce an area law for Wilson loops, provided that unevaluated terms to not cancel the effect found.

AB - The thermodynamic limit of lattice gauge theory is derived in a gauge which is optimized to make all link variables as close to unity as possible. The derivation rests upon (1) a precise bound on the fundamental modular region and (2) a direct evaluation of the functional integral of the Wilson lattice by the saddle-point method that is valid in the thermodynamic limit. The result confirms the calculational scheme obtained previously, which differs from the Faddeev-Popov scheme by the incorporation of non-perturbative effects, but which remains perturbatively renormalizable. The lattce Faddeev-Popov propagator, which appears in the modified action, acquires a dipole singularity at zero momentum, characteristic of long-range correlations. This is sufficient to produce an area law for Wilson loops, provided that unevaluated terms to not cancel the effect found.

UR - http://www.scopus.com/inward/record.url?scp=21344493490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344493490&partnerID=8YFLogxK

U2 - 10.1016/0920-5632(94)90343-3

DO - 10.1016/0920-5632(94)90343-3

M3 - Article

AN - SCOPUS:21344493490

VL - 34

SP - 198

EP - 200

JO - Nuclear and Particle Physics Proceedings

JF - Nuclear and Particle Physics Proceedings

SN - 2405-6014

IS - C

ER -