An Almost-Poisson Structure for Autoparallels on Riemann-Cartan Spacetime
GUO Yong-Xin1, SONG Yan-Bin1, ZHANG Xiao-Bin2, CHI Dong-Pyo3
1Department of Physics, Liaoning University, Shenyang 110036
2Faculty of Animal Science and Veterinany Medicine, Jinzhou Medical Science College, Jinzhou 121001
3Department of Mathematics, Seoul National University, Seoul 151-742, Korea
An Almost-Poisson Structure for Autoparallels on Riemann-Cartan Spacetime
1Department of Physics, Liaoning University, Shenyang 110036
2Faculty of Animal Science and Veterinany Medicine, Jinzhou Medical Science College, Jinzhou 121001
3Department of Mathematics, Seoul National University, Seoul 151-742, Korea
Abstract： 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.
(Canonical formalism, Lagrangians, and variational principles)
引用本文:
GUO Yong-Xin;SONG Yan-Bin;ZHANG Xiao-Bin;CHI Dong-Pyo. An Almost-Poisson Structure for Autoparallels on Riemann-Cartan Spacetime[J]. 中国物理快报, 2003, 20(8): 1192-1195.
GUO Yong-Xin, SONG Yan-Bin, ZHANG Xiao-Bin, CHI Dong-Pyo. An Almost-Poisson Structure for Autoparallels on Riemann-Cartan Spacetime. Chin. Phys. Lett., 2003, 20(8): 1192-1195.
2003, Vol. 20 
