Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1894301 | Journal of Geometry and Physics | 2009 | 19 Pages |
We consider the covariant quantization of generalized abelian gauge theories on a closed and compact nn-dimensional manifold whose space of gauge invariant fields is the abelian group of Cheeger–Simons differential characters. The space of gauge fields is shown to be a non-trivial bundle over the orbits of the subgroup of smooth Cheeger–Simons differential characters. Furthermore each orbit itself has the structure of a bundle over a multi-dimensional torus. As a consequence there is a topological obstruction to the existence of a global gauge fixing condition. A functional integral measure is proposed on the space of gauge fields which takes this problem into account and provides a regularization of the gauge degrees of freedom. For the generalized pp-form Maxwell theory closed expressions for all physical observables are obtained. The Green’s functions are shown to be affected by the non-trivial bundle structure. Finally the vacuum expectation values of circle-valued homomorphisms, including the Wilson operator for singular pp-cycles of the manifold, are computed and selection rules are derived.