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2000 | 51 | 1 | 283-292
Tytuł artykułu

Aspects of Geometric Quantization Theory in Poisson Geometry

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
51
Numer
1
Strony
283-292
Opis fizyczny
Daty
wydano
2000
Twórcy
autor
  • Department of Mathematics, University of Haifa, Israel
Bibliografia
  • [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.
  • [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.
  • [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.
  • [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.
  • [11] I. Vaisman, On the geometric quantization of the Poisson manifolds, J. Math. Phys. 32 (1991), 3339-3345.
  • [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.
  • [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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv51z1p283bwm
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