On the geometry of prequantization spaces
Zambon, Marco ; Zhu, Chenchang
arXiv, 0511187 / Harvested from arXiv
Text on arXiv
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 groupoid of $Q$ via an $S^1$ reduction that preserves both the groupoid and the geometric structure.
Publié le : 2005-11-07
Classification:  Mathematics - Differential Geometry,  Mathematical Physics,  53D17 
@article{0511187,
     author = {Zambon, Marco and Zhu, Chenchang},
     title = {On the geometry of prequantization spaces},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0511187}
}

Zambon, Marco; Zhu, Chenchang. On the geometry of prequantization spaces. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511187/