| Classical mechanics in non-commutative phase space |
| |
| 作者姓名： | 卫高峰 龙超云 隆正文 秦水介 付强 |
| |
| 作者单位： | Laboratory for Photoelectric Technology and Application Guizhou University，Guiyang 550025，China Department of Physics，College of Science，Guizhou University，Guiyang 550025，China，Laboratory for Photoelectric Technology and Application，Guizhou University，Guiyang 550025，China Department of Physics，College of Science，Guizhou University，Guiyang 550025，China，Laboratory for Photoelectric Technology and Application，Guizhou University，Guiyang 550025，China Department of Physics，College of Science，Guizhou University，Guiyang 550025，China，Laboratory for Photoelectric Technology and Application，Guizhou University，Guiyang 550025，China，Xi'an Technological University，Xi'an 710032，China |
| |
| 摘 要： | In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys. Rev. D, 2005, 72: 025010). The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative.
|
| 关 键 词： | non-commutative geometry classical mechanics free particle harmonic oscillator |
| 收稿时间： | 2007-6-29 |
| 修稿时间： | 2007-9-26 |
Classical mechanics in non-commutative phase space |
| |
| WEI Gao-Feng LONG Chao-Yun LONG Zheng-Wen QIN Shui-Jie FU Qiang.Classical mechanics in non-commutative phase space[J].High Energy Physics and Nuclear Physics,2008,32(5):338-341. |
| |
| Authors: | WEI Gao-Feng LONG Chao-Yun LONG Zheng-Wen QIN Shui-Jie FU Qiang |
| |
| Institution: | WEI Gao-Feng LONG Chao-Yun LONG Zheng-Wen QIN Shui-Jie FU Qiang 1 |
| |
| Abstract: | In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space.The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity.First,new Polsson brackets have been defined in non-commutative phase space.They contain corrections due to the non-commutativity of coordinates and momenta.On the basis of this new Poisson brackets,a new modified second law of Newton has been obtained.For two cases,the free particle and the harmonic oscillator,the equations of motion are derived on basis of the modified second law of Newton and the linear transformation(Phys.Rev.D,2005,72:025010).The consistency between both methods is demonstrated.It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space,but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative. |
| |
| Keywords: | non-commutative geometry classical mechanics free particle harmonic oscillator |
| 本文献已被 CNKI 维普 等数据库收录！ |
| 点击此处可从《中国物理 C》浏览原始摘要信息 |
| 点击此处可从《中国物理 C》下载免费的PDF全文 |
