Costratification in terms of coherent states
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Submission date: 15. May. 2014
published in: Journal of mathematical physics, 79 (2017) 2, p. 135-149
DOI number (of the published article): 10.1016/S0034-4877(17)30028-9
MSC-Numbers: 81S10, 81R30
Keywords and phrases: Quantum Theory, Hall Coherent States, Symmetry reduction
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Following the Hamiltonian approach on a finite spatial lattice, I construct a quantum gauge phase space with singularities and its quantum counterpart by the tool of Kähler quantization. Since the reduced phase space is a stratified Kähler space it is possible to construct a corresponding costratification on the quantum level which consists of a family of Hilbert subspaces corresponding to the strata in the classical phase space stratification. By means of Hall coherent states a new method for constructing a generating set of the costratified Hilbert space will be given, where each Hilbert subspace of the costratification corresponds to a certain subfamily of coherent states. Although the construction is applicable to all existing strata, it will be done explicitly for the case of point and toral stratum. For the simplest non abelian toy model with structure group SU(2) and at least two spatial plaquettes, these are the only occurring non generic strata.