# Aspects of Geometric Quantization Theory in Poisson Geometry

Banach Center Publications (2000)

- Volume: 51, Issue: 1, page 283-292
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topVaisman, Izu. "Aspects of Geometric Quantization Theory in Poisson Geometry." Banach Center Publications 51.1 (2000): 283-292. <http://eudml.org/doc/209040>.

@article{Vaisman2000,

abstract = {This is a survey exposition of the results of [14] on the relationship between the geometric quantization of a Poisson manifold, of its symplectic leaves and its symplectic realizations, and of the results of [13] on a certain kind of super-geometric quantization. A general formulation of the geometric quantization problem is given at the beginning.},

author = {Vaisman, Izu},

journal = {Banach Center Publications},

keywords = {polarization; super-geometric quantization; presymplectic realization; quantization triple; geometric quantization; symplectic leaves},

language = {eng},

number = {1},

pages = {283-292},

title = {Aspects of Geometric Quantization Theory in Poisson Geometry},

url = {http://eudml.org/doc/209040},

volume = {51},

year = {2000},

}

TY - JOUR

AU - Vaisman, Izu

TI - Aspects of Geometric Quantization Theory in Poisson Geometry

JO - Banach Center Publications

PY - 2000

VL - 51

IS - 1

SP - 283

EP - 292

AB - This is a survey exposition of the results of [14] on the relationship between the geometric quantization of a Poisson manifold, of its symplectic leaves and its symplectic realizations, and of the results of [13] on a certain kind of super-geometric quantization. A general formulation of the geometric quantization problem is given at the beginning.

LA - eng

KW - polarization; super-geometric quantization; presymplectic realization; quantization triple; geometric quantization; symplectic leaves

UR - http://eudml.org/doc/209040

ER -

## References

top- [1] P. Dazord, Réalisations isotropes de Libermann, Travaux du Séminaire Sud-Rhodanien de Géométrie II. Publ. Dept. Math. Lyon 4/B (1988), 1-52.
- [2] F. Guédira and A. Lichnerowicz, Géométrie des algèbres de Lie de Kirillov, J. Math. pures et appl. 63 (1984), 407-484. Zbl0562.53029
- [3] Y. Kerbrat and Z. Souici-Benhammadi, Variétés de Jacobi et groupoï des de contact, C. R. Acad. Sci. Paris, Sér. I 317 (1993), 81-86.
- [4] J. Huebschmann, Poisson cohomology and quantization, J. reine angew. Math. 408 (1990), 57-113.
- [5] A. Kirillov, Local Lie algebras, Russian Math. Surveys 31 (1976), 55-75. Zbl0357.58003
- [6] B. Kostant, Quantization and unitary representations, in: Lectures in modern analysis and applications III (C. T. Taam, ed.). Lect. Notes in Math. 170, Springer-Verlag, Berlin, Heidelberg, New York, 1970, 87-207.
- [7] A. Yu. Kotov, Remarks on geometric quantization of Poisson brackets of R-matrix type, Teoret. Mat. Fiz. 112 (2) (1997), 241-248 (in Russian). (Transl. Theoret. and Math. Phys. 112 (2) (1997), 988-994 (1998).)
- [8] M. de León, J. C. Marrero and E. Padrón, On the geometric quantization of Jacobi manifolds. J. Math. Phys. 38 (1997), 6185-6213. Zbl0898.58024
- [9] J. M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970.
- [10] I. Vaisman, Geometric quantization on spaces of differential forms, Rend. Sem. Mat. Torino 39 (1981), 139-152. Zbl0507.58026
- [11] I. Vaisman, On the geometric quantization of the Poisson manifolds, J. Math. Phys. 32 (1991), 3339-3345. Zbl0749.58023
- [12] I. Vaisman, Lectures on the geometry of Poisson manifolds, Progress in Math. 118, Birkhäuser, Basel, 1994.
- [13] I. Vaisman, Super-geometric quantization, Acta Math. Univ. Comenianae 64 (1995), 99-111.
- [14] I. Vaisman, On the geometric quantization of the symplectic leaves of Poisson manifolds, Diff. Geom. Appl. 7 (1997), 265-275. Zbl0901.58020
- [15] N. Woodhouse, Geometric Quantization, Clarendon Press, Oxford, 1980.
- [16] P. Xu, Gerstenhaber algebras and BV-algebras in Poisson geometry, Commun. Math. Physics 200 (1999), 545-560. Zbl0941.17016

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.