Gauge Fixing and the Gibbs Phenomenon
Jeffrey E. Mandula
Abstract
We address the question of why global gauge fixing, specifically to the lattice Landau gauge, becomes an extremely lengthy process 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.
Create a lesson
Related papers
Efficient Quantum Simulations of Yang-Mills theory with Maximal-tree Gauge
Tianyin Li, Ying-Ying Li, Xiaoyang Wang et al.
Physics-informed quantum algorithms for glueball-like excitations in a Z2 lattice gauge theory
Dan-Bo Zhang
Anomalous behavior of Wilson fermions in the presence of monopoles
Manuel Cortina, Rajamani Narayanan, Ray Romero
Direct lattice QCD calculation of the θ-induced CP-violating pion-nucleon coupling
Chuan-Yang Li, Jun Hua, Jian Liang et al.
Calculation of neutron electric dipole moment from Lattice QCD
Thomas Blum, Fangcheng He, Taku Izubuchi et al.
Exponential-in-Nc2 cost reduction of product-formula-based quantum simulations of quantum chromodynamics
Zohreh Davoudi, Jesse R. Stryker