Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1999-02-02
Physics
High Energy Physics
High Energy Physics - Lattice
6 pages; Talk given at XXIXth International Conference on High Energy Physics, Vancouver, 1998; Postscript format only, TeX no
Scientific paper
We discuss global gauge fixing on the lattice, specifically to the lattice Landau gauge, with the goal of understanding the question of why the process becomes extremely slow for large lattices. We construct an artificial "gauge-fixing" problem which has the essential features encountered in actuality. In the limit in which the size of the system to be gauge fixed becomes infinite, the problem becomes equivalent to finding a series expansion in functions which are related to the Jacobi polynomials. The series converges slowly, as expected. It also converges non-uniformly, which is an observed characteristic of gauge fixing. In the limiting example, the non-uniformity arises through the Gibbs phenomenon.
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