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Prog. Theor. Phys. Vol. 26 No. 2 (1961) pp. 157-172

Fixation of Physical Space-Time Coordinates and Equation of Motion of Two-Body Problem

Toshiei Kimura

Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima-ken

(Received January 28, 1961)

Abstract:

The consistency of the canonical reduction of gravitational field coupled with point particles is investigated. It is shown that the Hamiltonian, obtained by eliminating constraints and imposing coordinate condition, gives exactly the same equations of motion as obtained by Einstein, Infeld and Hoffmann. Furthermore, the derivation of the approximate (up to the fourth order of velocity of particle) equation of motion is presentd without tedious calculation.

URL : http://ptp.ipap.jp/link?PTP/26/157/
DOI : 10.1143/PTP.26.157

[ Full Text PDF : FREE ACCESS (856K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. The papers published by R. Arnowitt, S. Deser and C. W. Misner in a series are referred to as ADM-I, etc.
   (ADM-I) R. Arnowitt and S. Deser, Phys. Rev. 113 (1959), 745[APS].
   (ADM-II) R. Arnowitt, S. Deser and C. W. Misner, Phys. Rev. 116 (1959), 1322[APS].
   (ADM-III) R. Arnowitt, S. Deser and C. W. Misner, Phys. Rev. 117 (1960), 1959[APS].
   (ADM-IV) R. Arnowitt, S. Deser and C. W. Misner, Phys. Rev. 118 (1960), 1100[APS].
   (ADM-V) R. Arnowitt, S. Deser and C. W. Misner, Phys. Rev. 120 (1960), 313[APS].
   (ADM-Va) R. Arnowitt, S. Deser and C. W. Misner, Phys. Rev. 120 (1960), 321[APS].
2. A. Einstein, L. Infeld and B. Hoffmann, Ann. Math. 39 (1938), 66.
3. A. Papapetrou, Proc. Phys. Soc. 64 (1951), 57.
   V. Fock, The Theory of Space, Time and Gravitation (Pergamon Press, 1959), Chap. VI.
4. L. Infeld, Acta Phys. Polon. 13 (1954), 205; Rev. Mod. Phys. 29 (1957), 398[APS].
5. T. Kimura, Prog. Theor. Phys. 16 (1956), 157[PTP]; ibid. 16 (1956), 555[PTP].
6. E. Corinaldesi, Proc. Phys. Soc. 69 (1956), 190.
7. R. Arnowitt, S. Deser and C. W. Misner, J. Math. Phys. 1 (1960), 434[CrossRef].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 26 No. 5 (1961) pp. 790-792 :

   On a Fixation of Gauge and True Observables of Yang-Mills Field

   Toshiei Kimura

2. Progress of Theoretical Physics Vol. 27 No. 4 (1962) pp. 747-771 :

   Introduction of True Variables and Consistency of Hamiltonian Formalism

   Toshiei Kimura

3. Progress of Theoretical Physics Vol. 33 No. 3 (1965) pp. 510-523 :

   An Attempt to Derive the Gravitational Potential

   Toshiei Kimura

4. Progress of Theoretical Physics Vol. 48 No. 1 (1972) pp. 316-328 :

   Potential in the Canonical Formalism of Gravity

   Toshiei Kimura and Takehiro Toiya

5. Progress of Theoretical Physics Vol. 51 No. 5 (1974) pp. 1598-1612 :

   Coordinate Condition and Higher Order Gravitational Potential in Canonical Formalism

   Tadayuki Ohta, Hiroshi Okamura, Toshiei Kimura and Kichiro Hiida

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