Ultraviolet filtering of lattice configurations and applications to Monte Carlo dynamics

TL;DR

This paper introduces a filtering method using Dirac quasi-zero-modes to reduce noise in lattice configurations, preserving classical solutions and enabling better analysis of topological structures like instantons.

Contribution

The paper presents a novel filtering technique based on Dirac quasi-zero-modes that effectively reduces noise without distorting classical solutions in lattice gauge configurations.

Findings

The filtering method preserves solutions of classical equations of motion.

It significantly reduces short-wavelength stochastic noise in Monte Carlo configurations.

The method enables detailed study of topological structures such as instantons.

Abstract

We present a detailed study of a filtering method based upon Dirac quasi-zero-modes in the adjoint representation. The procedure induces no distortions on configurations which are solutions of the euclidean classical equations of motion. On the other hand, it is very effective in reducing the short-wavelength stochastic noise present in Monte Carlo generated configurations. After testing the performance of the method in various situations, we apply it successfully to study the effect of Monte Carlo dynamics on topological structures like instantons.