Quantum Algebra and Topology
[Submitted on 24 May 1995 (v1), last revised 8 Jun 1995 (this version, v2)]
Title:On the quantization of Poisson brackets
View PDFAbstract: In this paper we introduce two classes of Poisson brackets on algebras (or on sheaves of algebras). We call them locally free and nonsingular Poisson brackets. Using the Fedosov's method we prove that any locally free nonsingular Poisson bracket can be quantized. In particular, it follows from this that all Poisson brackets on an arbitrary field of characteristic zero can be quantized. The well known theorem about the quantization of nondegenerate Poisson brackets on smooth manifolds follows from the main result of this paper as well.
Submission history
From: Donin Joseph [view email][v1] Wed, 24 May 1995 13:34:06 UTC (1 KB) (withdrawn)
[v2] Thu, 8 Jun 1995 10:31:03 UTC (17 KB)
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