Fedosov *-Products and Quantum Momentum Maps
Fedosov *-Products and Quantum Momentum Maps
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DOI：
10.1007/s002200050446
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发表时间：
1996-08
影响因子：
2.4
通讯作者：
P. Xu
中科院分区：
文献类型：
--
作者：
P. Xu
本文的目的是研究与Fedosov方法有关的辛流形上星积的各个方面。通过引入“量子指数映射”的概念，我们给出了费多索夫连接的一个表征。作为应用，得到了任意*积与费多索夫*积等价的几何实现。每个费多索夫*积都被证明是一个维*积。因此，我们发现每个*积都等价于一个Vey *积，这是Lichnerowicz的经典结果。研究了哈密顿空间的量子化，特别是量子动量映射。研究了形变量化下的拉格朗日子流形。
The purpose of this paper is to study various aspects of star products on a symplectic manifold related to the Fedosov method. By introducing the notion of “quantum exponential maps” we give a characterization of Fedosov connections. As an application, a geometric realization is obtained for the equivalence between an arbitrary *-product and a Fedosov one. Every Fedosov *-product is shown to be a Vey *-product. Consequently, we find that every *-product is equivalent to a Vey *-product, a classical result of Lichnerowicz. Quantization of a hamiltonianG-space, and in particular, quantum momentum maps are studied. Lagrangian submanifolds are also studied under a deformation quantization.