Gauge-invariant discrete models of Yang-Mills equations
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.
scientific article; zbMATH DE number 1238051