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Prog. Theor. Phys. Vol. 20 No. 5 (1958) pp. 690-702

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Dispersion Relations and Vertex Properties in Perturbation Theory

K. Symanzik

Max-Planck-Institut für Physik, Göttingen, Germany

(Received July 17, 1958)

Abstract:

Dispersion relations for nucleon-nucleon scattering with momentum transfer 2|Δ| < µ, for meson-nucleon scattering, and related properties of the meson-nucleon vertex, are shown to hold in every order perturbation theory. This is done by extending a method used by Nambu to discuss the perturbation-theoretical parametric representations of Green's function. In effect arbitrarily complicated Feynman diagrams are reduced to a few simple types.


URL : http://ptp.ipap.jp/link?PTP/20/690/
DOI : 10.1143/PTP.20.690

[ Full Text PDF : FREE ACCESS (712K) ] Citation:

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References:

  1. Y. Nambu, Nuovo Cimento 6 (1957), 1064.
  2. E.g. G.F. Chew, R. Karplus, S. Gasiorowicz, F. Zachariasen, Phys. Rev. 110 (1958), 265[APS]; V. Glaser, B. Jakišić, Nuovo Cimento 5 (1957), 1197.
  3. J. Schwinger, Proceedings of the Seventh Annual Rochester Conference, Sec. IV.
  4. J. S. R. Chisholm, Proc. Cambr. Phil. Soc. 48 (1952) 300 a. 518.
  5. R. J. Eden, Proc. Roy. Soc. Ld. A 210 (1952), 388.
  6. J. Hamilton, Proc. Cambr. Phil. Soc. 48 (1952), 640.
  7. E.g. H. Lehmann, Phys. Rev. (in press). This paper contains further references, especially to the fundamental papers by N. N. Bogoliubov et al.
  8. K. Symanzik, Nuovo Cimento 5 (1957), 659.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 21 No. 1 (1959) pp. 135-150 :
    On the Validity of Dispersion Relations in Perturbation Theory
    Noboru Nakanishi
  2. Progress of Theoretical Physics Vol. 22 No. 1 (1959) pp. 128-144 :
    Ordinary and Anomalous Thresholds in Perturbation Theory
    Noboru Nakanishi
  3. Progress of Theoretical Physics Vol. 22 No. 2 (1959) pp. 247-273 :
    Electromagnetic Structure of the Nucleon. I
    Kichiro Hiida, Noboru Nakanishi, Yukihisa Nogami and Masayuki Uehara
  4. Progress of Theoretical Physics Vol. 23 No. 5 (1960) pp. 942-956 :
    Dispersion Relations in Nucleon-Nucleon Scattering
    Yasuo Hara and Hironari Miyazawa
  5. Progress of Theoretical Physics Vol. 26 No. 3 (1961) pp. 337-355 :
    Integral Representations for Scattering Amplitudes in Perturbation Theory
    Noboru Nakanishi
  6. Progress of Theoretical Physics Vol. 27 No. 4 (1962) pp. 682-692 :
    The Mass Spectral Condition and Analytic Properties of the Vertex Function
    Gaku Konisi
  7. Progress of Theoretical Physics Vol. 42 No. 4 (1969) pp. 966-977 :
    Feynman-Parametric Formula for the Hankel-Transformed Position-Space Feynman Integral
    Noboru Nakanishi

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