Geometric quantization on presymplectic manifolds

Izu Vaisman

doi:10.1007/BF01471212

Geometric quantization on presymplectic manifolds

Izu Vaisman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we discuss the possibilities of adapting geometric quantization to presymplectic manifolds, i.e., differentiable manifolds M^2n+k (k>0) endowed with a closed 2-form ω of rank 2n. We show that such an adaptation is possible in various manners, and that, as a general idea, it reduces the quantization on M to quantization on the symplectic quotient M/V, where V is the foliation defined by the annihilator of ω.

Original language	English
Pages (from-to)	293-310
Number of pages	18
Journal	Monatshefte fur Mathematik
Volume	96
Issue number	4
DOIs	https://doi.org/10.1007/BF01471212
State	Published - Dec 1983

ASJC Scopus subject areas

General Mathematics

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10.1007/BF01471212

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title = "Geometric quantization on presymplectic manifolds",

abstract = "In this paper, we discuss the possibilities of adapting geometric quantization to presymplectic manifolds, i.e., differentiable manifolds M2n+k (k>0) endowed with a closed 2-form ω of rank 2n. We show that such an adaptation is possible in various manners, and that, as a general idea, it reduces the quantization on M to quantization on the symplectic quotient M/V, where V is the foliation defined by the annihilator of ω.",

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AB - In this paper, we discuss the possibilities of adapting geometric quantization to presymplectic manifolds, i.e., differentiable manifolds M2n+k (k>0) endowed with a closed 2-form ω of rank 2n. We show that such an adaptation is possible in various manners, and that, as a general idea, it reduces the quantization on M to quantization on the symplectic quotient M/V, where V is the foliation defined by the annihilator of ω.

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DO - 10.1007/BF01471212

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Geometric quantization on presymplectic manifolds

Abstract

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