Non-commutative phase space and its space-time symmetry

• Published in: Chinese physics C Vol. 34; no. 7; pp. 944 - 948
• Main Author: 李康 沙依甫加马力·达吾来提
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.07.2010; Department of Physics, Hangzhou Normal University, Hangzhou, 310036, China%School of Physics Science and Technology, Xinjiang University, Urumqi, 830046, China
• Subjects: 庞加莱; 时空对称性; 洛仑兹变换; 相空间; 非交换; non-commutative phase space; space-time symmetry; Lorentz transformation
• ISSN: 1674-1137; 0254-3052; 2058-6132
• DOI: 10.1088/1674-1137/34/7/003

First a description of 2＋1 dimensional non-commutative（NC） phase space is presented,and then we find that in this formulation the generalized Bopp＇s shift has a symmetric representation and one can easily and straightforwardly define the star product on NC phase space. Then we define non-commutative Lorentz transformations both on NC space and NC phase space. We also discuss the Poincare symmetry. Finally we point out that our NC phase space formulation and the NC Lorentz transformations are applicable to any even dimensional NC space and NC phase space.