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Prog. Theor. Phys. Vol. 46 No. 6 (1971) pp. 1885-1904

[ Full Text PDF : FREE ACCESS (1200K) ]

Substitution Law and Identity for Long-Range Potentials

Kichiro Hiida and Hiroshi Okamura

Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo

(Received July 22, 1971)

Abstract:

We discuss the relations between two-body and many-body static potentials for long-range interactions. There is a simple substitution law to get the two-body potential V2(2n) in the 2n-th order from (n+1)-body potential vn+1 obtained from tree diagrams for (n+1)-body scatterings. When interaction Lagrangian density is proportional to mass in the static limit, the identity Vn+1=V2(2n) holds, Vn+1 being the two-body potential obtained from vn+1 by summing it up over all elementary particles in two celestial bodies or charged spheres. These statements are proved to be right for n=2 and partly for n=3, and expected to be true for all values of n. The reason why the substitution law exists and the identity holds is discussed in detail.


URL : http://ptp.ipap.jp/link?PTP/46/1885/
DOI : 10.1143/PTP.46.1885

[ Full Text PDF : FREE ACCESS (1200K) ] Citation:

References:

  1. Y. Iwasaki, Lett. Nuovo Cim. 1 (1971), 783; Prog. Theor. Phys. 46 (1971), 1587[PTP].
  2. A. Einstein, L. Infeld and B. Hoffman, Ann. Math. 39 (1938), 66.
  3. K. Hiida and M. Kikugawa, Prog. Theor. Phys. 46 (1971), 1610[PTP].
  4. H. Lehmann, Nuovo Cim. 11 (1954), 342.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 47 No. 5 (1972) pp. 1743-1757 :
    Gauge Transformation and Gravitational Potentials
    Kichiro Hiida and Hiroshi Okamura
  2. Progress of Theoretical Physics Vol. 48 No. 1 (1972) pp. 316-328 :
    Potential in the Canonical Formalism of Gravity
    Toshiei Kimura and Takehiro Toiya
  3. Progress of Theoretical Physics Vol. 48 No. 2 (1972) pp. 662-677 :
    Gravitational Field in the Unified Spinor Field Theory
    Yasuhisa Katayama and Hiroshi Kokubo
  4. Progress of Theoretical Physics Vol. 51 No. 4 (1974) pp. 1220-1238 :
    Higher Order Gravitational Potential for Many-Body System
    Tadayuki Ohta, Hiroshi Okamura, Toshiei Kimura and Kichiro Hiida

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