On the geometric quantization of Poisson manifolds
On the geometric quantization of Poisson manifolds
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泊松流形的几何量化
DOI：
10.1063/1.529446
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发表时间：
1991
影响因子：
1.3
通讯作者：
I. Vaisman
中科院分区：
文献类型：
--
作者：
I. Vaisman
在Huebschmann的一篇论文中[J. Reine Angew. 408，57（1990）]，泊松流形的几何量子化作为泊松代数量子化的一个特例出现。在这里，这种量化是直截了当地提出的。结果包括一个几何预量化完整性条件和讨论在特定情况下，如狄拉克括号，适应的概念的极化和建设的量子希尔伯特空间，和计算的例子。在本文的最后一节中，我们描述了Poisson流形和Jacobi流形的Urwin [Adv.Math.50，126（1983）]意义下的一般预量子化表示。
In a paper by Huebschmann [J. Reine Angew. Math. 408, 57 (1990)], the geometric quantization of Poisson manifolds appears as a particular case of the quantization of Poisson algebras. Here, this quantization is presented straightforwardly. The results include a geometric prequantization integrality condition and its discussion in particular cases such as Dirac brackets, an adaptation of the notion of a polarization and a construction of a quantum Hilbert space, and a computational example. In the last section of the paper the general prequantization representations in the sense of Urwin [Adv. Math. 50, 126 (1983)] are described for the Poisson and Jacobi manifolds.