Self-Dual and Anti-Self-Dual Solutions of Discrete Yang-Mills Equations on a Double Complex

Abstract

We study a discrete model of the SU(2) Yang-Mills equations on a combinatorial analog of â„⁴. Self-dual and anti-self-dual solutions of discrete Yang-Mills equations are constructed. To obtain these solutions we use both techniques of a double complex and the quaternionic approach. Interesting analogies between instanton, anti-instanton solutions of discrete and continual self-dual, anti-self-dual equations are also discussed.