Classical mechanics in non-commutative phase space

被引：0

作者：

卫高峰 ^{[1
]}

龙超云 ^{[1
]}

隆正文 ^{[1
]}

秦水介 ^{[2
]}

付强 ^{[3
]}

机构：

[1] Laboratory for Photoelectric Technology and Application,Guizhou University,Guiyang 550025,China Department of Physics,College of Science,Guizhou University,Guiyang 550025,China

[2] Laboratory for Photoelectric Technology and Application,Guizhou University,Guiyang 550025,China

[3] Xi'an Technological University,Xi'an 710032,China

来源：

Chinese Physics C | 2008年 / 05期

基金：

中国国家自然科学基金;

关键词：

non-commutative geometry; classical mechanics; free particle; harmonic oscillator;

D O I：

暂无

中图分类号：

O316 [分析力学（解析力学）];

学科分类号：

080101 ;

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 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.

引用

页码：338 / 341

页数：4

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