Abelian gauge theories on compact manifolds and the Gribov ambiguity

Details Abelian gauge theories on compact manifolds and the Gribov ambiguity Abelian gauge theories on compact manifolds and the Gribov ambiguity

2007-07-09

arxiv.org/abs/0707.1186v1

J.Math.Phys.49:052302,2008

Physics

High Energy Physics

High Energy Physics - Theory

33 pages

Scientific paper

10.1063/1.2909197

We study the quantization of abelian gauge theories of principal torus bundles over compact manifolds with and without boundary. It is shown that these gauge theories suffer from a Gribov ambiguity originating in the non-triviality of the bundle of connections whose geometrical structure will be analyzed in detail. Motivated by the stochastic quantization approach we propose a modified functional integral measure on the space of connections that takes the Gribov problem into account. This functional integral measure is used to calculate the partition function, the Greens functions and the field strength correlating functions in any dimension using the fact that the space of inequivalent connections itself admits the structure of a bundle over a finite dimensional torus. The Greens functions are shown to be affected by the non-trivial topology, giving rise to non-vanishing vacuum expectation values for the gauge fields.

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