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

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.


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
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