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Bloch Waves in Minimal Landau Gauge and the Infinite-Volume Limit of Lattice Gauge Theory

Attilio Cucchieri and Tereza Mendes
Phys. Rev. Lett. 118, 192002 – Published 9 May 2017

Abstract

By exploiting the similarity between Bloch’s theorem for electrons in crystalline solids and the problem of Landau gauge fixing in Yang-Mills theory on a “replicated” lattice, we show that large-volume results can be reproduced by simulations performed on much smaller lattices. This approach, proposed by Zwanziger [Nucl. Phys. B412, 657 (1994)], corresponds to taking the infinite-volume limit for Landau-gauge field configurations in two steps: first for the gauge transformation alone, while keeping the lattice volume finite, and second for the gauge-field configuration itself. The solutions to the gauge-fixing condition are then given in terms of Bloch waves. Applying the method to data from Monte Carlo simulations of pure SU(2) gauge theory in two and three space-time dimensions, we are able to evaluate the Landau-gauge gluon propagator for lattices of linear extent up to 16 times larger than that of the simulated lattice. This approach is reminiscent of the Fisher-Ruelle construction of the thermodynamic limit in classical statistical mechanics.

  • Figure
  • Received 7 December 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.192002

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Attilio Cucchieri and Tereza Mendes

  • Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, SP, Brazil

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Issue

Vol. 118, Iss. 19 — 12 May 2017

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