Vol.5 No.4 (July 2015)
The Study on Particle’s Equations of Motion in the Space-Time with Torsion
陈方培 ：大连理工大学物理与光电技术学院，辽宁 大连
The process of deriving the particle’s equations of motion in the space-time with torsion can be formulated as the following four steps: first, writing the Lagrangian of matter field and gravitational field for the physical system; second, calculating the energy-momentum tensor density of matter field; third, writing the particle’s momentum, and using the Dirac delta function, the relations between energy-momentum tensor density of the matter field and its particle’s momentum can be found; fourth, considering the Lagrangian symmetry and conservation law of the physical system the relations among energy-momentum tensor density and generalized spin density, and space-time curvature, and torsion can be found. From this relation, the equations of motion for the particle in the space-time with torsion can be derived. In order to clarify some people’s misun-derstanding of the equations of motion for particles in space-time with torsion, we mainly explain the theoretical basis of the above four steps in this article. And this paper will also show that the particle’s equations of motion in general relativity are the special case of particle’s equations of motion in torsional gravity, and the particle’s equations of motion in the special relativity are the special case of particle’s equations of motion in general relativity.
陈方培 (2015) 有挠时空理论中质点运动方程研究。 现代物理， 5， 73-78. doi: 10.12677/MP.2015.54010
 陈方培 (2014) 时空与物质——物理学的基本概念和基本规律. 科学出版社, 北京.
 Landau, L.D. and Lif-shitz, E.M. (1975) The classical theory of fields. Translated by Hamermesh, M. Pergamon Press, Oxford.
 福克, 著 (1965) 空间、时间和引力的理论. 周培源, 等, 译. 科学出版社, 北京.
 Hehl, F.W., von der Heyde, P., Kerlick, G.D. and Nester, J.M. (1976) General relativity with spin and torsion: Foundations and prospects. Reviews of Modern Physics, 48, 393-416. http://dx.doi.org/10.1103/RevModPhys.48.393
 Chen, F.P. (1990) General equations of motion for test particles in space-time with torsion. International Journal of Theoretical Physics, 29, 161-171.
 Weinberg, S. (1972) Gravitation and cosmology. Wiley, New York.
 Kibble, T.W.B. (1961) Lorentz invariance and the gravitational field. Journal of Mathematical Physics, 2, 212-221. http://dx.doi.org/10.1063/1.1703702
 陈方培, 任洪梅, 时家国 (1993) 视广义相对论及新广义相对论为广义引力理论特殊情况的研究. 大连理工大学学报, 3, 269-275.