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arXiv · hep-th/9511197

Quasi-Local Formulation of Non-Abelian Finite-Element Gauge Theory

Kimball A. Milton
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Abstract

Recently it was shown how to formulate the finite-element equations of motion of a non-Abelian gauge theory, by gauging the free lattice difference equations, and simultaneously determining the form of the gauge transformations. In particular, the gauge-covariant field strength was explicitly constructed, locally, in terms of a path ordered product of exponentials (link operators). On the other hand, the Dirac and Yang-Mills equations were nonlocal, involving sums over the entire prior lattice. Earlier, Matsuyama had proposed a local Dirac equation constructed from just the above-mentioned link operators. Here, we show how his scheme, which is closely related to our earlier one, can be implemented for a non-Abelian gauge theory. Although both Dirac and Yang-Mills equations are now local, the field strength is not. The technique is illustrated with a direct calculation of the current anomalies in two and four space-time dimensions. Unfortunately, unlike the original finite-element proposal, this scheme is in general nonunitary.

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Kimball A. Milton. 1995-11-28. Quasi-Local Formulation of Non-Abelian Finite-Element Gauge Theory. https://doi.org/10.1103/physrevd.53.5898

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