Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21583
Zambon, M; Zhu, C (2007). On the geometry of prequantization spaces. Journal of Geometry and Physic, 57(11):2372-2397.
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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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|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|
|Deposited On:||04 Jan 2010 13:42|
|Last Modified:||05 Apr 2016 13:23|
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