FIELD STRENGTH FORMULATION OF SU(2) YANG–MILLS THEORY IN THE MAXIMAL ABELIAN GAUGE: PERTURBATION THEORY

M. QUANDT, H. REINHARDT
1998 International Journal of Modern Physics A  
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
more » ... 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.
doi:10.1142/s0217751x9800189x fatcat:tb5bnebqyzcz3k57bdzgpz2t3q