Prog. Theor. Phys. Vol. 64 No. 3 (1980) pp. 883-896

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Gravity from Poincaré Gauge Theory of the Fundamental Particles. II

— Equations of Motion for Test Bodies and Various Limits —

Institute of Physics, University of Tokyo, Komaba, Tokyo 153
^*Physics Department, Saitama University, Urawa, Saitama 338

(Received March 27, 1980)

Abstract:

We study the equations of motion for test bodies and various limits in Poincaré gauge theory with linear and quadratic Lagrangians. The classical equations of motion are derived both for spin-1/2 particles and for macroscopic test bodies. It is also shown that various limits can be taken, including General Relativity and New General Relativity.

URL : http://ptp.ipap.jp/link?PTP/64/883/
DOI : 10.1143/PTP.64.883

References:

K. Hayashi and T. Shirafuji, Prog. Theor. Phys. 64 (1980), 866[PTP].
P. J. Roll, R. Krotkov and R. H. Dicke, Ann. of Phys. 26 (1964), 442[CrossRef].
V. B. Braginsky and V. I. Panov, Zh. Eksp. i Teor. Fiz. 61 (1971), 873 [Sov. Phys.-JETP 34 (1971), 464].
K. S. Thorne and C. M. Will, Astrophys. J. 163 (1971), 595[CrossRef].
K. Hayashi and T. Shirafuji, Phys. Rev. D 19 (1979), 3524[APS].
W. Pauli, Helv. Phys. Acta 5 (1932), 179.
See also Section III of Ref. 4).
The Hamilton-Jacobi equation in classical mechanics is treated in, for example, H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1950).
Application to particle motion in General Relativity can be found in C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).
S. I. Rubinow and J. B. Keller, Phys. Rev. 131 (1963), 2789[APS].
K. Rafanelli and R. Shiller, Phys. Rev. 135 (1964), B279[APS].
K. Hayashi and A. Bregman, Ann. of Phys. 75 (1973), 562[CrossRef].
H. Weyl, Phys. Rev. 77 (1950), 699[APS].
For a review, see F. W. Hehl, P. von der Heyde, G. D. Kerlick and J. M. Nester, Rev. Mod. Phys. 48 (1976), 393[APS].
For the classical gravitational field, see R. Utiyama and B. S. DeWitt, J. Math. Phys. 3 (1962), 608[CrossRef].
For the quantized gravitational field, see S. Deser, in Proceedings of the Conference on Gauge Theories and Modern Field Theory, edited by R. Arnowitt and P. Nath (MIT Press, Cambridge, Mass., 1976);
S. Weinberg, in Proceedings of the XVII International Conference on High Energy Physics, edited by J. R. Smith (Rutherford Laboratory, Chilton, 1974).
K. S. Stelle, Phys. Rev. D 16 (1977), 953[APS].

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