Instanton-anti-instanton solutions of discrete Yang-Mills equations. (English) Zbl 1265.39010

Sushch, Volodymyr

Math. Bohem. 137, No. 2, 219-228 (2012).

Summary: We study a discrete model of the \(\mathrm{SU}(2)\) Yang-Mills equations on a combinatorial analog of \(\mathbb {R}^4\). Self-dual and anti-self-dual solutions of discrete Yang-Mills equations are constructed. To obtain these solutions we use both the techniques of a double complex and the quaternionic approach.

MSC:

39A12	Discrete version of topics in analysis
81T13	Yang-Mills and other gauge theories in quantum field theory

Keywords:

Yang-Mills equation; self-dual equation; anti-self-dual equation; instanton; anti-instanton; difference equation