  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
$\beta$-function for the running coupling constant in this approach and
reproduce the standard result.
