Aspects of Geometric Quantization Theory in Poisson Geometry

Izu Vaisman

Banach Center Publications (2000)

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

Abstract

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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.

How to cite

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Vaisman, 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

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  3. [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. [4] J. Huebschmann, Poisson cohomology and quantization, J. reine angew. Math. 408 (1990), 57-113. 
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  7. [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. [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. [9] J. M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970. 
  10. [10] I. Vaisman, Geometric quantization on spaces of differential forms, Rend. Sem. Mat. Torino 39 (1981), 139-152. Zbl0507.58026
  11. [11] I. Vaisman, On the geometric quantization of the Poisson manifolds, J. Math. Phys. 32 (1991), 3339-3345. Zbl0749.58023
  12. [12] I. Vaisman, Lectures on the geometry of Poisson manifolds, Progress in Math. 118, Birkhäuser, Basel, 1994. 
  13. [13] I. Vaisman, Super-geometric quantization, Acta Math. Univ. Comenianae 64 (1995), 99-111. 
  14. [14] I. Vaisman, On the geometric quantization of the symplectic leaves of Poisson manifolds, Diff. Geom. Appl. 7 (1997), 265-275. Zbl0901.58020
  15. [15] N. Woodhouse, Geometric Quantization, Clarendon Press, Oxford, 1980. 
  16. [16] P. Xu, Gerstenhaber algebras and BV-algebras in Poisson geometry, Commun. Math. Physics 200 (1999), 545-560. Zbl0941.17016

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