Super symplectic geometry and prequantization

[摘要] We review the prequantization procedure in the context of symplectic supermanifolds 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 vertical bar 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. (C) 2010 Elsevier B.V. All rights reserved.

[发布日期] 2010-12-01

[关键词] Symplectic supermanifolds;Prequantization;Non-homogeneous symplectic superforms