Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-02-02
Commun.Math.Phys.286:459-494,2009
Physics
High Energy Physics
High Energy Physics - Theory
38 pages, 9 figures. Changes: comments on the heat kernel and coherent states have been added
Scientific paper
10.1007/s00220-008-0693-0
In the Hamiltonian approach on a single spatial plaquette, we construct a quantum (lattice) gauge theory which incorporates the classical singularities. The reduced phase space is a stratified K\"ahler space, and we make explicit the requisite singular holomorphic quantization procedure on this space. On the quantum level, this procedure furnishes a costratified Hilbert space, that is, a Hilbert space together with a system which consists of the subspaces associated with the strata of the reduced phase space and of the corresponding orthoprojectors. The costratified Hilbert space structure reflects the stratification of the reduced phase space. For the special case where the structure group is $\mathrm{SU}(2)$, we discuss the tunneling probabilities between the strata, determine the energy eigenstates and study the corresponding expectation values of the orthoprojectors onto the subspaces associated with the strata in the strong and weak coupling approximations.
Huebschmann Johannes
Rudolph Gerd
Schmidt Matthias
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