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A gauge-invariant discrete analog of the Yang-Mills equations on a double complex

Volodymyr Sushch
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Abstract

An intrinsically defined gauge-invariant discrete model of the Yang-Mills equations on a combinatorial analog of $\Bbb{R}^4$ is constructed. We develop several algebraic structures on the matrix-valued cochains (discrete forms) that are analogs of objects in differential geometry. We define a combinatorial Hodge star operator based on the use of a double complex construction. Difference self-dual and anti-self-dual equations will be given. In the last section we discus the question of generalizing our constructions to the case of a 4-dimensional combinatorial sphere

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Volodymyr Sushch. 2006-11-08. A gauge-invariant discrete analog of the Yang-Mills equations on a double complex. https://arxiv.org/abs/math-ph/0611019

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