预量化的变化
Variations on Prequantization
摘要：
通过定义Dirac流形P的预量子化为具有相容Dirac-Jacobi结构的主U（1）-丛Q，我们推广了Poisson流形和前辛流形的预量子化过程.利用Hamilton向量场，研究了P上容许函数的Poisson代数在Q上各种局部（关于P）定义函数空间上的作用.最后，在复分析和接触几何中出现的例子的指导下，我们提出了预量子化概念的一个扩展，其中允许U（1）对Q的作用有一些不动点。
英文摘要：
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.
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