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Prog. Theor. Phys. Vol. 13 No. 3 (1955) pp. 305-328

[ Full Text PDF : FREE ACCESS (1485K) ]

Many-Body Problem in Quantum Field Theory, III

Kazuhiko Nishijima

Department of Physics, Osaka City University, Osaka

(Received February 15, 1955)

Abstract:

The general procedures described in I and II to deal with the scattering problems involving composite particles are illustrated in this paper for the interacting scalar meson and scalar photon fields.
Utilizing Wick's solution for the covariant two-body equation (Bethe-Salpeter equation), the following problems are discussed:
(1) the normalization of the Feynman amplitude for the bound state corresponding to Wick's solution,
(2) the disintegration of the bound state by a scalar photon,
(3) the Rutherford scattering of the composite particle.
In appendices some general remarks are given on the reciprocal nature of the present formalism and on the asymptotic forms of the Feynman emplitudes.


URL : http://ptp.ipap.jp/link?PTP/13/305/
DOI : 10.1143/PTP.13.305

[ Full Text PDF : FREE ACCESS (1485K) ] Citation:

References:

  1. K. Nishijima, Prog. Theor. Phys. 10 (1953), 549[PTP]; ibid. 12 (1954), 279[PTP].
    These papers are cited as I and II respectively. Earlier references are given in these papers.
  2. R. P. Feynman, Phys. Rev. 76 (1949), 749[APS]; ibid. 76 (1949), 769[APS].
  3. E. E. Salpeter and H. A. Bethe, Phys. Rev. 84 (1951), 1232[APS].
  4. G. C. Wick, Phys. Rev. 96 (1954), 1124[APS].
    His method is further generalized to other bound states by
    R. E. Cutkosky, Phys. Rev. 96 (1954), 1135[APS].
    Similar calculations have ever been made by Hayashi and Munakata, but in their treatment the propagation function DF was replaced by the function D.
    C. hayashi and Y. Munakata, Prog. Theor. Phys. 7 (1951), 481[PTP].
  5. J. Schwinger, Proc. Natl. Acad. Sci. 37 (1951), 452; ibid. 37 (1951), 455.
  6. G. C. Wick, Phys. Rev. 80 (1950), 268[APS].
  7. M. Gell-Mann and F. Low, Phys. Rev. 84 (1951), 350[APS].
  8. K. Nishijima, Prog. Theor. Phys. 8 (1952), 401[PTP].
  9. C. Møller, Kgl. Danske Videnskab. Mat. -Fys. Medd. 23 (1945), No. 1.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 15 No. 3 (1956) pp. 237-254 :
    On the Use of Feynman Amplitudes in the Quantum Field Theory
    Ziro Maki
  2. Progress of Theoretical Physics Vol. 16 No. 6 (1956) pp. 667-683 :
    On a Theory of a Composite Model of Elementary Particles
    Ziro Maki
  3. Progress of Theoretical Physics Vol. 17 No. 6 (1957) pp. 765-802 :
    On the Asymptotic Conditions in Quantum Field Theory
    Kazuhiko Nishijima
  4. Progress of Theoretical Physics Vol. 22 No. 1 (1959) pp. 73-88 :
    Approximate Solution of the Relativistic Two-Body Equation and its Application to the Nuclear Forces
    Hiroshi Yamamoto
  5. Progress of Theoretical Physics Vol. 22 No. 2 (1959) pp. 159-167 :
    Multipole Model of Elementary Particles. I
    Daisuke Ito, Shigeo Minami and Hiroshi Tanaka
  6. Progress of Theoretical Physics Vol. 23 No. 4 (1960) pp. 629-661 :
    One-Particle Motions in Many-Particle Systems and the Optical Model in Nuclear Reactions
    Mikio Namiki
  7. Progress of Theoretical Physics Vol. 25 No. 2 (1961) pp. 178-188 :
    Approximate Solution of the Bethe-Salpeter Equation for Two Fermions
    Masaaki Kawaguchi
  8. Progress of Theoretical Physics Vol. 36 No. 4 (1966) pp. 799-819 :
    Propagator and Vertex Function of a Bound State in the Green's Function Formalism
    Noboru Nakanishi
  9. Progress of Theoretical Physics Vol. 40 No. 3 (1968) pp. 620-627 :
    Normalization of the Degenerate B-S Amplitudes
    Jiro Arafune
  10. Progress of Theoretical Physics Vol. 40 No. 3 (1968) pp. 628-639 :
    S-Matrix and Abnormal Solutions of the Bethe-Salpeter Equation
    Seiichi Naitô
  11. Progress of Theoretical Physics Vol. 43 No. 1 (1970) pp. 184-205 :
    An Attempt at a General Theory of the Bethe-Salpeter Equation
    Masakuni Ida
  12. Progress of Theoretical Physics Vol. 55 No. 5 (1976) pp. 1514-1525 :
    Threshold Behavior of the Structure Functions in a Composite Model Field Theory
    Masao Ninomiya and Keiji Watanabe
  13. Progress of Theoretical Physics Vol. 119 No. 2 (2008) pp. 263-284 :
    Zero-Energy Solutions of the Bethe-Salpeter Equation for a Spinor-Scalar System Exchanging Photons
    G. B. Mainland

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