Gauge-invariant discrete models of Yang-Mills equations. (English. Russian original) Zbl 0935.53017

Sushch, V. N.

Math. Notes 61, No. 5, 621-631 (1997); translation from Mat. Zametki 61, No. 5, 742-754 (1997).

The author constructs two discrete analogues of the Yang-Mills equations in \(\mathbb{R}^n\) for some matrix Lie group \(G\), and defines a discrete analog of the operator of exterior covariant differentiation. This operator is used to construct a model satisfying the gauge invariance principle. Also, for the developed discrete model, a result which is similar to the one of the continuous model is provided, stating that for a four-dimensional initial manifold the Yang-Mills theory can be regarded as a nonlinear generalization of the Hodge theory.

Reviewer: V.Balan (Bucureşti)

MSC:

53C07	Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
81T13	Yang-Mills and other gauge theories in quantum field theory
39A12	Discrete version of topics in analysis

Keywords:

discrete analog; Yang-Mills equations; gauge invariance; discrete model; Yang-Mills theory; Hodge theory

References:

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