| An Almost—Poisson Structure for Autoparallels on Riemann—Cartan Spacetime |
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| 引用本文： | 郭永新 宋彦彬 张晓滨 CHIDong-Pyo.An Almost—Poisson Structure for Autoparallels on Riemann—Cartan Spacetime[J].中国物理快报,2003,20(8):1192-1195. |
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| 作者姓名： | 郭永新 宋彦彬 张晓滨 CHIDong-Pyo |
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| 作者单位： | [1]DepartmentofPllysics,LiaoningUniversity,Shenyang110036 [2]FacultyofAnimalScienceandVeterinaryMedicine,JinzhouMedicalScienceCollege,Jinzhou121001 [3]DepartmentofMathematics,SeoulNationalUniversity,Seoul151-742,Korea |
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| 摘 要： | An almost-Poisson bracket is constructed for the regular Hamiltonian formulation of autoparallels on Riemann-Cartan spacetime, which is considered to be the motion trajectory of spinless particles in the space. This bracket satisfies the usual properties of a Poisson bracket except for the Jacobi identity. There does not exist a usual Poisson structure for the system although a special Lagrangian can be found for the case that the contracted torsion tensor is a gradient of a scalar field and the traceless part is zero. The almost-Poisson bracket is decomposed into a sum of the usual Poisson bracket and a “Lie-Poisson“ bracket, which is applied to obtain a formula for the Jacobiizer and to decompose a non-Hamiltonian dynamical vector field for the system. The almost-Poisson structure is also globally formulated by means of a pseudo-symplectic two-form on the cotangent bundle to the spacetime manifold.
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| 关 键 词： | Riemann－Cartan时空 泊松结构 分析力学 哈密顿系统 自平行规则 运动轨迹 非完整系统 |
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