Discrete models of the self-dual and anti-self-dual equations

TL;DR

This paper develops a gauge-invariant discrete model for Yang-Mills theory and constructs difference equations representing self-dual and anti-self-dual conditions.

Contribution

It introduces a novel discrete framework for Yang-Mills equations that preserves gauge invariance and captures self-duality properties.

Findings

Discrete self-dual equations are explicitly constructed.

The model maintains gauge invariance in the discrete setting.

Potential applications in numerical simulations of gauge theories.

Abstract

In the case of a gauge-invariant discrete model of Yang-Mills theory difference self-dual and anti-self-dual equations are constructed.