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Field Strength Formulation of SU(2) Yang-Mills Theory in the Maximal Abelian Gauge: Perturbation Theory

M. Quandt·H. Reinhardt
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Abstract

We present a reformulation of SU(2) Yang-Mills theory in the maximal Abelian gauge, where the non-Abelian gauge field components are exactly integrated out at the expense of a new Abelian tensor field. The latter can be treated in a semiclassical approximation and the corresponding saddle point equation is derived. Besides the non-trivial solutions, which are presumably related to non-perturbative interactions for the Abelian gauge field, the equation of motion for the tensor fields allows for a trivial solution as well. We show that the semiclassical expansion around this trivial solution is equivalent to the standard perturbation theory. In particular, we calculate the one-loop $β$-function for the running coupling constant in this approach and reproduce the standard result.

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M. Quandt, H. Reinhardt. 1998-02-02. Field Strength Formulation of SU(2) Yang-Mills Theory in the Maximal Abelian Gauge: Perturbation Theory. https://doi.org/10.1142/s0217751x9800189x

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