Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-07-22
Int.J.Mod.Phys. A13 (1998) 4049-4076
Physics
High Energy Physics
High Energy Physics - Theory
29 pages LaTeX, 6 postscript figures. Version to be published in Int. J. Mod. Phys. A
Scientific paper
10.1142/S0217751X9800189X
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.
Quandt Markus
Reinhardt Hugo
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