Non-commutative phase space and its space-time symmetry

  • 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.

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LI Kang, Dulat Sayipjamal and Non-commutative phase space and its space-time symmetry[J]. Chinese Physics C, 2010, 34(7): 944-948. doi: 10.1088/1674-1137/34/7/003
LI Kang, Dulat Sayipjamal and Non-commutative phase space and its space-time symmetry[J]. Chinese Physics C, 2010, 34(7): 944-948.  doi: 10.1088/1674-1137/34/7/003 shu
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Received: 2009-07-28
Revised: 2009-11-25
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Non-commutative phase space and its space-time symmetry

    Corresponding author: LI Kang,

Abstract: 

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.

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