A gauge-invariant discrete analog of the Yang-Mills equations on a double complex. (English) Zbl 1139.81375

Sushch, Volodymyr

Cubo 8, No. 3, 61-78 (2006).

Summary: An intrinsically defined gauge-invariant discrete model of the Yang-Mills equations on a combinatorial analog of \(\mathbb R^4\) 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 discuss the question of generalizing our constructions to the case of a 4-dimensional combinatorial sphere.

MSC:

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