Abstract
We study gauge fixing via the standard local extremization algorithm for 2-dimensional U(1). On a lattice with spherical topology S{sup 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. ((orig.)).
Forcrand, P de;
[1]
Hetrick, J E
[2]
- Eidgenoessische Technische Hochschule, Zurich (Switzerland). Interdisciplinary Project Center for Supercomputing
- Physics Dept., University of Arizona, Tucson, AZ 85721 (United States)
Citation Formats
Forcrand, P de, and Hetrick, J E.
The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition.
Netherlands: N. p.,
1995.
Web.
doi:10.1016/0920-5632(95)00404-W.
Forcrand, P de, & Hetrick, J E.
The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition.
Netherlands.
https://doi.org/10.1016/0920-5632(95)00404-W
Forcrand, P de, and Hetrick, J E.
1995.
"The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition."
Netherlands.
https://doi.org/10.1016/0920-5632(95)00404-W.
@misc{etde_101032,
title = {The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition}
author = {Forcrand, P de, and Hetrick, J E}
abstractNote = {We study gauge fixing via the standard local extremization algorithm for 2-dimensional U(1). On a lattice with spherical topology S{sup 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. ((orig.)).}
doi = {10.1016/0920-5632(95)00404-W}
journal = []
volume = {42}
journal type = {AC}
place = {Netherlands}
year = {1995}
month = {Apr}
}
title = {The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition}
author = {Forcrand, P de, and Hetrick, J E}
abstractNote = {We study gauge fixing via the standard local extremization algorithm for 2-dimensional U(1). On a lattice with spherical topology S{sup 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. ((orig.)).}
doi = {10.1016/0920-5632(95)00404-W}
journal = []
volume = {42}
journal type = {AC}
place = {Netherlands}
year = {1995}
month = {Apr}
}