Abstract
In a paper by Huebschmann [J. Reine Angew. Math. 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. 50, 126 (1983)] are described for the Poisson and Jacobi manifolds.
Original language | English |
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Pages (from-to) | 3339-3345 |
Number of pages | 7 |
Journal | Journal of Mathematical Physics |
Volume | 32 |
Issue number | 12 |
DOIs | |
State | Published - 1991 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics