A gauge model for quantum mechanics on a stratified space

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dc.creatorHuebschmann, J.
dc.creatorRudolph, G.
dc.creatorSchmidt, M.
dc.date2007-02-02
dc.date2008-11-07
dc.date.accessioned2026-07-07T12:35:44Z
dc.date.available2026-07-07T12:35:44Z
dc.descriptionIn 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 Kähler 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.
dc.description38 pages, 9 figures. Changes: comments on the heat kernel and coherent states have been added
dc.identifierhttps://arxiv.org/abs/hep-th/0702017
dc.identifierhttp://arxiv.org/abs/hep-th/0702017
dc.identifierCommun.Math.Phys.286:459-494,2009
dc.identifierdoi:10.1007/s00220-008-0693-0
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217858
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleA gauge model for quantum mechanics on a stratified space
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