On the geometry of prequantization spaces

JOURNAL OF GEOMETRY AND PHYSICS

卷:57

Article

Zambon, Marco ; Zhu, Chenchang

关键词: Dirac manifolds;    lie algebroid;    prequantization;    Jacobi-Dirac manifolds;    precontact groupoids;   

DOI  :  10.1016/j.geomphys.2007.08.003

来源: Elsevier

【 摘 要 】

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 S-1 reduction that preserves both the Lie groupoid and the geometric structures. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free