Super Symplectic Geometry and Prequantization
Document type :
Pré-publication ou Document de travail
Permalink :
Title :
Super Symplectic Geometry and Prequantization
Author(s) :
HAL domain(s) :
Mathématiques [math]/Physique mathématique [math-ph]
Physique [physics]/Physique mathématique [math-ph]
Physique [physics]/Physique mathématique [math-ph]
English abstract : [en]
We review the prequantization procedure in the context of super symplectic manifolds with a symplectic form which is not necessarily homogeneous. In developing the theory of non homogeneous symplectic forms, there is one ...
Show more >We review the prequantization procedure in the context of super symplectic manifolds with a symplectic form which is not necessarily homogeneous. In developing the theory of non homogeneous symplectic forms, there is one surprising result: the Poisson algebra no longer is the set of smooth functions on the manifold, but a subset of functions with values in a super vector space of dimension 1|1. We show that this has no notable consequences for results concerning coadjoint orbits, momentum maps, and central extensions. Another surprising result is that prequantization in terms of complex line bundles and prequantization in terms of principal circle bundles no longer are equivalent if the symplectic form is not even.Show less >
Show more >We review the prequantization procedure in the context of super symplectic manifolds with a symplectic form which is not necessarily homogeneous. In developing the theory of non homogeneous symplectic forms, there is one surprising result: the Poisson algebra no longer is the set of smooth functions on the manifold, but a subset of functions with values in a super vector space of dimension 1|1. We show that this has no notable consequences for results concerning coadjoint orbits, momentum maps, and central extensions. Another surprising result is that prequantization in terms of complex line bundles and prequantization in terms of principal circle bundles no longer are equivalent if the symplectic form is not even.Show less >
Language :
Anglais
Comment :
40 pages; AMSTeX
Collections :
Source :
Submission date :
2025-01-24T18:32:50Z
Files
- 0306049
- Open access
- Access the document