Variations on Prequantization
Symplectic Geometry
2007-05-23 v1 Differential Geometry
Abstract
We extend known prequantization procedures for Poisson and presymplectic manifolds by defining the prequantization of a Dirac manifold P as a principal U(1)-bundle Q with a compatible Dirac-Jacobi structure. We study the action of Poisson algebras of admissible functions on P on various spaces of locally (with respect to P) defined functions on Q, via hamiltonian vector fields. Finally, guided by examples arising in complex analysis and contact geometry, we propose an extension of the notion of prequantization in which the action of U(1) on Q is permitted to have some fixed points.
Cite
@article{arxiv.math/0412502,
title = {Variations on Prequantization},
author = {Alan Weinstein and Marco Zambon},
journal= {arXiv preprint arXiv:math/0412502},
year = {2007}
}
Comments
33 pages; contribution to the proceedings of the conference Poisson 2004