DEFORMATION QUANTIZATION OF POISSON MANIFOLDS IN THE DERIVATIVE EXPANSION

被引：1

作者：

Bratchikov, A. V. ^{[1
]}

机构：

[1] Kuban State Technol Univ, Krasnodar 350072, Russia

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2009年 / 6卷 / 02期

关键词：

Deformation quantization; non-commutative geometry;

D O I：

10.1142/S0219887809003485

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Deformation quantization of Poisson manifolds is studied within the framework of an expansion in powers of derivatives of Poisson structures. We construct the Lie group associated with a Poisson bracket algebra which defines a second order deformation in the derivative expansion.

引用

页码：219 / 224

页数：6

共 7 条

[1] DEFORMATION THEORY AND QUANTIZATION .1. DEFORMATIONS OF SYMPLECTIC STRUCTURES [J].

BAYEN, F ;

FLATO, M ;

FRONSDAL, C ;

LICHNEROWICZ, A ;

STERNHEIMER, D .

ANNALS OF PHYSICS, 1978, 111 (01) :61-110

[2]

Bourbaki N., 1972, Groupes et algebres de Lie

[3] A SIMPLE GEOMETRICAL CONSTRUCTION OF DEFORMATION QUANTIZATION [J].

FEDOSOV, BV .

JOURNAL OF DIFFERENTIAL GEOMETRY, 1994, 40 (02) :213-238

[4] AN EXPLICIT STAR-PRODUCT ON THE COTANGENT BUNDLE OF A LIE GROUP [J].

GUTT, S .

LETTERS IN MATHEMATICAL PHYSICS, 1983, 7 (03) :249-258

[5]

KATHOTIA V, MATHQA9811174

[6] Deformation quantization of Poisson manifolds [J].

Kontsevich, M .

LETTERS IN MATHEMATICAL PHYSICS, 2003, 66 (03) :157-216

[7]

PENKAVA M, MATHQA9804022

← 1 →