A gauge model for quantum mechanics on a stratified space

Abstract

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 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.

38 pages, 9 figures. Changes: comments on the heat kernel and coherent states have been added

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Cited by in corpus (11)

• Free particles from Brauer algebras in complex matrix models
• Dynamics for QCD on an infinite lattice
• Operator-algebraic construction of gauge theories and Jones' actions of Thompson's groups
• On the algebra of quantum observables for a certain gauge model
• Defining relations for the orbit type strata of SU(2)-lattice gauge models
• On the Reflection Type Decomposition of the Adjoint Reduced Phase Space of a Compact Semisimple Lie group
• Gauge Orbit Types for Theories with Classical Compact Gauge Group
• The Hilbert space costratification for the orbit type strata of SU(2)-lattice gauge theory
• Quantum lattice gauge fields and groupoid C*-algebras
• Singular symplectic cotangent bundle reduction of gauge field theory
• Quasicharacters, recoupling calculus and costratifications of lattice quantum gauge theory