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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
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| Cite this article: |
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GUO Yong-Xin, SONG Yan-Bin, ZHANG Xiao-Bin et al 2003 Chin. Phys. Lett. 20 1192-1195 |
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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.
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| Keywords:
03.20.+i
04.20.Fy
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Published: 01 August 2003
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| PACS: |
03.20.+i
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04.20.Fy
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(Canonical formalism, Lagrangians, and variational principles)
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