Self-dual and anti-self-dual solutions of discrete Yang-Mills equations on a double complex

Details Self-dual and anti-self-dual solutions of discrete Yang-Mills equations on a double complex Self-dual and anti-self-dual solutions of discrete Yang-Mills equations on a double complex

2009-09-16

arxiv.org/abs/0909.3114v1

Physics

Mathematical Physics

17 pages

Scientific paper

We study a discrete model of the SU(2) Yang-Mills equations on a combinatorial analog of $\Bbb{R}^4$. 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.

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