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 held components are exactly integrated out at the expense of a new Abelian tensor held. The latter can be treated in a semiclassical approximation and the corresponding saddle point equation is derived. Besides the nontrivial solutions, which are presumably related to nonperturbative 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 beta-function for the running coupling constant in this approach and reproduce the standard result.