QUANTIZATION OF SINGULAR REDUCTION

被引：3

作者：

Bates, L. ^{[1
]}

Cushman, R. ^{[1
]}

Hamilton, M. ^{[1
]}

Sniatycki, J. ^{[1
]}

机构：

[1] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada

来源：

REVIEWS IN MATHEMATICAL PHYSICS | 2009年 / 21卷 / 03期

关键词：

Singular reduction; algebraic reduction; geometric quantization; decomposition of quantization representation; differential space; GEOMETRIC-QUANTIZATION; GROUP-REPRESENTATIONS; POISSON ALGEBRAS; SPACES; MULTIPLICITIES; COHOMOLOGY;

D O I：

10.1142/S0129055X09003633

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper creates a theory of quantization of singularly reduced systems. We compare our results with those obtained by quantizing algebraically reduced systems. In the case of a Kahler polarization, we show that quantization of a singularly reduced system commutes with reduction, thus generalizing results of Sternberg and Guillemin. We illustrate our theory by treating an example of Arms, Gotay and Jennings where algebraic and singular reduction at the zero level of the momentum mapping differ. In spite of this, their quantizations agree.

引用

页码：315 / 371

页数：57

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