An Almost-Poisson Structure for Autoparallels on Riemann-Cartan Spacetime
An Almost-Poisson Structure for Autoparallels on Riemann-Cartan Spacetime
复制标题
DOI：
10.1088/0256-307x/20/8/302
复制
发表时间：
2003-08
影响因子：
3.5
通讯作者：
Guo Yong-xin;Song Yan-Bin;Zhang Xiaobin;Chi Dong-Pyo
中科院分区：
文献类型：
--
作者：
Guo Yong-xin;Song Yan-Bin;Zhang Xiaobin;Chi Dong-Pyo
对黎曼-卡尔坦时空上自平行线的正则哈密顿公式构造了一个几乎泊松支架，认为这是空间中无自旋粒子的运动轨迹。除了雅可比恒等式外，这个括号满足泊松括号的一般性质。当压缩扭转张量是标量场的梯度且无迹部分为零时，可以找到一个特殊的拉格朗日量，但该系统不存在通常的泊松结构。将近泊松括号分解为通常的泊松括号和“Lie-Poisson”括号的和，利用它得到Jacobiizer的公式，并分解出系统的非哈密顿动力向量场。利用时空流形的余切束上的伪辛二型，对近似泊松结构进行了全局表述。
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.