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 S 1 reduction that preserves both the Lie groupoid and the geometric structures.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
