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