On the Fedosov deformation quantization beyond the regular Poisson manifolds

被引：5

作者：

Dolgushev, VA ^{[1
]}

Isaev, AP

Lyakhovich, SL

Sharapov, AA

机构：

[1] Joint Inst Nucl Res, Bogoliubov Lab Theoret Phys, Dubna 141980, Moscow Region, Russia

[2] Inst Theoret & Expt Phys, Moscow 117259, Russia

[3] Max Planck Inst Math, D-53111 Bonn, Germany

[4] Chalmers Univ Technol, Dept Theoret Phys, S-41296 Gothenburg, Sweden

[5] Tomsk VV Kuibyshev State Univ, Dept Theoret Phys, Tomsk 634050, Russia

来源：

NUCLEAR PHYSICS B | 2002年 / 645卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

deformation quantization; quantum groups;

D O I：

10.1016/S0550-3213(02)00763-0

中图分类号：

O412 [相对论、场论]; O572.2 [粒子物理学];

学科分类号：

摘要：

A simple iterative procedure is suggested for the deformation quantization of (irregular) Poisson brackets associated to the classical Yang-Baxter equation. The construction is shown to admit a pure algebraic reformulation giving the Universal Deformation Formula (UDF) for any triangular Lie bialgebra. A simple proof of classification theorem for inequivalent UDF's is given. As an example the explicit quantization formula is presented for the quasi-homogeneous Poisson brackets on two-plane. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：457 / 476

页数：20

共 29 条

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