ScholarLens Back to search
1994•CERN Document Server (European Organization for Nuclear Research)Requires access

The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition

Philippe de Forcrand, Hetrick, J E

Open publisher page 11 citations

Abstract

We study gauge fixing via the standard local extremization algorithm for 2-dimensional U(1). On a lattice with spherical topology S^2 where all copies are lattice artifacts, we find that the number of these 'Gribov' copies diverges in the continuum limit. On a torus, we show that lattice artifacts can lead to the wrong evaluation of the gauge-invariant correlation length, when measured via a gauge-fixed procedure; this bias does not disappear in the continuum limit. We then present a new global approach, based on Hodge decomposition of the gauge field, which produces a unique smooth field in Landau gauge, and is economically powered by the FFT. We also discuss the use of this method for examining topological objects, and its extensions to non-abelian gauge fields.

About this research paper

What this paper is about

We study gauge fixing via the standard local extremization algorithm for 2-dimensional U(1). On a lattice with spherical topology S^2 where all copies are lattice artifacts, we find that the number of these 'Gribov' copies diverges in the continuum limit. On a torus, we show that lattice artifacts can lead to the wrong evaluation of the gauge-invariant correlation length, when measured via a gauge-fixed procedure; this bias does not disappear in the continuum limit. We then present a new global approach, based on Hodge decomposition of the gauge field, which produces a unique smooth field in Landau gauge, and is economically powered by the FFT. We also discuss the use of this method for examining topological objects, and its extensions to non-abelian gauge fields.

Why it matters

OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We study gauge fixing via the standard local extremization algorithm for 2-dimensional U(1). On a lattice with spherical topology S^2 where all copies are lattice artifacts, we find that the number of these 'Gribov' copies diverges in the continuum limit. On a torus, we show that lattice artifacts can lead to the wrong evaluation of the gauge-invariant correlation length, when measured via a gauge-fixed procedure; this bias does not disappear in the continuum limit. We then present a new global approach, based on Hodge decomposition of the gauge field, which produces a unique smooth field in Landau gauge, and is economically powered by the FFT. We also discuss the use of this method for examining topological objects, and its extensions to non-abelian gauge fields.

Key concepts: Lattice (music), Lattice gauge theory, Gauge theory, Mathematics, Lattice field theory, Torus, Abelian group, Hamiltonian lattice gauge theory

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition — Research Paper | ScholarLens