On the geometric quantization of Poisson manifolds

Journal Article · Sat Nov 30 23:00:00 EST 1991 · Journal of Mathematical Physics (New York); (United States)

DOI:https://doi.org/10.1063/1.529446· OSTI ID:5019794

Vaisman, I ^[1]

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1. Department of Mathematics, University of Haifa (Israel)

In a paper by Huebschmann (J. Reine Angew. Math. {bold 408}, 57 (1990)), the geometric quantization of Poisson manifolds appears as a particular case of the quantization of Poisson algebras. Here, this quantization is presented straightforwardly. The results include a geometric prequantization integrality condition and its discussion in particular cases such as Dirac brackets, an adaptation of the notion of a polarization and a construction of a quantum Hilbert space, and a computational example. In the last section of the paper the general prequantization representations in the sense of Urwin (Adv. Math. {bold 50}, 126 (1983)) are described for the Poisson and Jacobi manifolds.

• OSTI ID: 5019794
• Journal Information: Journal of Mathematical Physics (New York); (United States), Journal Name: Journal of Mathematical Physics (New York); (United States) Vol. 32:12; ISSN 0022-2488; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BANACH SPACE
CLASSICAL MECHANICS
COMMUTATION RELATIONS
COMMUTATORS
FUNCTIONS
GEOMETRY
HAMILTONIAN FUNCTION
HILBERT SPACE
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
MECHANICS
QUANTIZATION
QUANTUM MECHANICS
QUANTUM OPERATORS
SPACE
SYMMETRY GROUPS
VECTOR FIELDS