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On the geometry of prequantization spaces


Zambon, M; Zhu, C (2007). On the geometry of prequantization spaces. Journal of Geometry and Physic, 57(11):2372-2397.

Abstract

Given a Poisson (or more generally Dirac) manifold P, there are two approaches to its geometric quantization: one involves a circle bundle Q over P endowed with a Jacobi (or Jacobi–Dirac) structure; the other one involves a circle bundle with a (pre)contact groupoid structure over the (pre)symplectic groupoid of P. We study the relation between these two prequantization spaces. We show that the circle bundle over the (pre)symplectic groupoid of P is obtained from the Lie groupoid of Q via an S1 reduction that preserves both the Lie groupoid and the geometric structures.

Abstract

Given a Poisson (or more generally Dirac) manifold P, there are two approaches to its geometric quantization: one involves a circle bundle Q over P endowed with a Jacobi (or Jacobi–Dirac) structure; the other one involves a circle bundle with a (pre)contact groupoid structure over the (pre)symplectic groupoid of P. We study the relation between these two prequantization spaces. We show that the circle bundle over the (pre)symplectic groupoid of P is obtained from the Lie groupoid of Q via an S1 reduction that preserves both the Lie groupoid and the geometric structures.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Dirac manifolds; Lie algebroid; Prequantization; Jacobi–Dirac manifolds; Precontact groupoids
Language:English
Date:2007
Deposited On:04 Jan 2010 13:42
Last Modified:05 Apr 2016 13:23
Publisher:Elsevier
ISSN:0393-0440
Publisher DOI:https://doi.org/10.1016/j.geomphys.2007.08.003
Related URLs:http://arxiv.org/abs/math/0511187

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