HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 17 (1957) > Number 3
| Next Article >

Prog. Theor. Phys. Vol. 17 No. 3 (1957) pp. 401-418

[ Full Text PDF : FREE ACCESS (1161K) ]

General Integral Formula of Perturbation Term in the Quantized Field Theory

Noboru Nakanishi

Department of Physics, Kyoto University, Kyoto

(Received October 15, 1956)

Abstract:

An arbitrary perturbation term in the quantized field theory is expressed explicitly in terms of generalized Feynman parametric integral, after all integrations of momenta are carried out. By means of this general integral formula Dyson's power-counting theorem as well as the absence of odd order divergences are proved rigorously, and Lehmann's spectral function ρ(u) is given explicitly in perturbation expansion. Some remarks are made on the convergence of perturbation series.


URL : http://ptp.ipap.jp/link?PTP/17/401/
DOI : 10.1143/PTP.17.401

[ Full Text PDF : FREE ACCESS (1161K) ] Citation:

References:

  1. F. J. Dyson, Phys. Rev. 75 (1949), 1736[APS].
  2. R. P. Feynman, Phys. Rev. 76 (1949), 769[APS].
  3. Y. Nambu, Phys. Rev. 100 (1955), 394[APS].
  4. H. Lehmann, Nuovo Cim. 11 (1954), 342.
  5. C. A. Hurst, Proc. R. Soc. A 214 (1952), 44; Proc. Camb. Phil. Soc. 48 (1952), 625.
  6. W. Thirring, Helv. Phys. Acta 26 (1953), 33.
  7. M. A. Petermann, Helv. Phys. Acta 26 (1953), 291.
  8. L. Schwartz, Théorie des Distributions (1950).
  9. N. Nakanishi, Soryushiron Kenkyu (mimeographed circular in Japanese) 12 (1956), 217.
  10. V. Weisskopf, Phys. Rev. 56 (1939), 72[APS].
  11. R. Utiyama and I. Imamura, Prog. Theor. Phys. 9 (1953), 431[PTP].
    R. Utiyama, Prog. Theor. Phys. 9 (1953), 593[PTP].
  12. A. Salam and P. T. Matthews, Phys. Rev. 90 (1953), 690[APS].
  13. S. F. Edwards, Phil. Mag. 45 (1954), 758; ibid. 46 (1955), 569.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 19 No. 2 (1958) pp. 159-168 :
    General Theory of Infrared Divergence
    Noboru Nakanishi
  2. Progress of Theoretical Physics Vol. 20 No. 2 (1958) pp. 239-241 :
    On a Non-Adiabatic Approximate Method in the Non-Linear Interaction Theory
    Shoji Ozaki
  3. Progress of Theoretical Physics Vol. 21 No. 1 (1959) pp. 135-150 :
    On the Validity of Dispersion Relations in Perturbation Theory
    Noboru Nakanishi
  4. Progress of Theoretical Physics Vol. 22 No. 1 (1959) pp. 128-144 :
    Ordinary and Anomalous Thresholds in Perturbation Theory
    Noboru Nakanishi
  5. 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
  6. Progress of Theoretical Physics Vol. 22 No. 3 (1959) pp. 351-372 :
    Electromagnetic Structure of the Nucleon. II
    Kichiro Hiida, Noboru Nakanishi, Yukihisa Nogami and Masayuki Uehara
  7. Progress of Theoretical Physics Vol. 22 No. 6 (1959) pp. 863-881 :
    Electromagnetic Structure of the Nucleon. III
    Kichiro Hiida and Noboru Nakanishi
  8. Progress of Theoretical Physics Vol. 23 No. 2 (1960) pp. 284-286 :
    A Note on the Ordinary and Anomalous Thresholds in Perturbation Theory
    Noboru Nakanishi
  9. Progress of Theoretical Physics Vol. 24 No. 6 (1960) pp. 1275-1295 :
    On the Validity of Multiple Dispersion Representations
    Noboru Nakanishi
  10. Progress of Theoretical Physics Vol. 25 No. 2 (1961) pp. 277-289 :
    New Analyses of Anomalous Imaginary Part
    Jun Otokozawa
  11. Progress of Theoretical Physics Vol. 25 No. 2 (1961) pp. 296-297 :
    Validity of the Integral Representations for the Vertex Part in Perturbation Theory
    Noboru Nakanishi
  12. Progress of Theoretical Physics Vol. 25 No. 6 (1961) pp. 981-988 :
    Dispersion Relations and High Energy Limits in Quantum Field Theory. III
    Seiya Aramaki
  13. Progress of Theoretical Physics Vol. 26 No. 3 (1961) pp. 391-417 :
    A Simple Model for Two-Channel Reaction in Field Theory and Its Application to the Y* Problem
    Yasunori Fujii
  14. 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
  15. Progress of Theoretical Physics Vol. 52 No. 1 (1974) pp. 304-312 :
    Integrability and Regularization in Local Field Theory
    Kunio Yamamoto
  16. Progress of Theoretical Physics Vol. 60 No. 3 (1978) pp. 840-850 :
    Meson Regge Trajectories in the Quark-Gluon Model
    Yasuo Oishi

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.