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

Attilio Cucchieri; Tereza Mendes

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1612.01279 v1 pith:N2NLS6ZP submitted 2016-12-05 hep-lat

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

Attilio Cucchieri , Tereza Mendes This is my paper

classification hep-lat

keywords latticegaugeblochinfinite-volumelimittheoryableapproach

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

0 comments

read the original 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, one is able to obtain essentially infinite-volume results from numerical simulations performed on a relatively small lattice. This approach, proposed by D. Zwanziger in \cite{Zwanziger:1993dh}, corresponds to taking the infinite-volume limit for Landau-gauge field configurations in two steps: firstly for the gauge transformation alone, while keeping the lattice volume finite, and secondly 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 sixteen times larger than that of the simulated lattice. The approach is reminiscent of Fisher and Ruelle's construction of the thermodynamic limit in classical statistical mechanics.

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Birman-Schwinger Formulation of the Faddeev-Popov Zero-Mode Problem
hep-th 2026-07 conditional novelty 6.0

The first Gribov horizon of a transverse gauge background equals the first appearance of −1 in the spectrum of a normalized Birman-Schwinger operator, via an inertia-preserving congruence rather than a similarity.