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Reduction and eigenstates in deformation quantization. (English) Zbl 0809.58012

Demuth, Michael (ed.) et al., Pseudo-differential calculus and mathematical physics. Berlin: Akademie-Verlag. Math. Top. 5, 277-297 (1994).
The author considers a Hamiltonian that satisfies, at the classical level, a number of special conditions thereby giving rise to a specific fibration of phase space. In this situation, the process of Hamiltonian reduction is considered in terms of deformation quantum algebras. It is suggested to use an index theorem for deformation quantum algebras with twisted coefficients for investigating topological and spectral properties of the Hamiltonian.
For the entire collection see [Zbl 0797.00001].
Reviewer: V.Perlick (Berlin)

MSC:

53D55 Deformation quantization, star products
70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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