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

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. 1 Supported in part by DFG under contract Re 856/1-3. 2 Supported by “Graduiertenkolleg: Hadronen und Kerne”.