HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Supplement (1961) > No.18
| Next Article >

Prog. Theor. Phys. Supplement No.18 (1961) pp. 1-81

[ Full Text PDF : FREE ACCESS (3839K) ]

Parametric Integral Formulas and Analytic Properties in Perturbation Theory

Noboru Nakanishi

Research Institute for Fundamental Physics, Kyoto University, Kyoto

(Received February 20, 1961)

Abstract:

The general term in perturbation theory is explicitly given in terms of the Feynman parametric integral. The properties of the parametric functions appearing in this integral are investigated in detail. By using this formula, systematic investigations on the singularities of the general term are extensively developed. Dispersion relations for various forward and non-forward scatterings (and vertex functions) and some other integral representations for the vertex function are proved in every order of perturbation theory.


URL : http://ptp.ipap.jp/link?PTPS/18/1/
DOI : 10.1143/PTPS.18.1

[ Full Text PDF : FREE ACCESS (3839K) ] Citation:

References:

  1. H. J. Bremermann, R. Oehme and J. G. Taylor, Phys. Rev. 109 (1958), 2178[APS].
  2. R. Karplus, C. M. Sommerfield and E. H. Wichmann, Phys. Rev. 111 (1958), 1187[APS].
  3. R. Oehme, Phys. Rev. 111 (1958), 1430[APS].
  4. Y. Nambu, Nuovo Cim. 9 (1958), 610.
  5. F. J. Dyson, Phys. Rev. 106 (1957), 157[APS].
  6. G. Feldman, Proc. R. Soc. (London) A 233 (1954), 112.
  7. N. Nakanishi, Prog. Theor. Phys. 19 (1958), 607[PTP].
  8. N. Nakanishi, Prog. Theor. Phys. 21 (1959), 135[PTP].
  9. S. Mandelstam, Phys. Rev. 112 (1958), 1344[APS].
  10. N. Nakanishi, Prog. Theor. Phys. 17 (1957), 401[PTP]. See also N. Nakanishi, Soryushiron Kenkyu (mimeographed circular in Japanese) 12 (1956), 217; ibid. 13 (1956), 89.
  11. N. Nakanishi, Prog. Theor. Phys. 22 (1959), 128[PTP].
  12. N. Nakanishi, Prog. Theor. Phys. 23 (1960), 284[PTP].
  13. R. P. Feynman, Phys. Rev. 76 (1949), 769[APS].
  14. R. Chisholm, Proc. Camb. Phil. Soc. 48 (1952), 300 [Errata; 48 (1952), 518].
  15. C. A. Hurst, Proc. R. Soc. (London) A 214 (1952), 44.
    C. A. Hurst, Proc. Camb. Phil. Soc. 48 (1952), 625.
  16. W. Thirring, Helv. Phys. Acta 26 (1953), 33.
  17. M. A. Petermann, Helv. Phys. Acta 26 (1953), 291.
  18. Y. Nambu, Nuovo Cim. 6 (1957), 1064.
  19. K. Symanzik, Prog. Theor. Phys. 20 (1958), 690[PTP].
  20. L. Schwartz, Theorie des Distributions I, II (1950, Paris Herman).
  21. K. Hiida, N. Nakanishi, Y. Nogami and M. Uehara, Prog. Theor. Phys. 22 (1959), 351[PTP].
  22. R. J. Eden, Proc. R. Soc. (London) A 210 (1952), 388.
  23. J. Hamilton, Proc. Camb. Phil. Soc. 48 (1952), 640.
  24. L. D. Landau, Nucl. Phys. 13 (1959), 181[CrossRef].
  25. L. B. Okun and A. P. Rudik, Nucl. Phys. 15 (1960), 261[Elsevier].
  26. J. C. Taylor, Phys. Rev. 117 (1960), 261[APS].
  27. J. C. Polkinghorne and G. R. Screaton, Nuovo Cim. 15 (1960), 289; ibid. 15 (1960), 925.
  28. R. J. Eden, Phys. Rev. 119 (1960), 1763[APS].
  29. M. Lévy, Nuovo Cim. 13 (1959), 115.
  30. J. Mathews, Phys. Rev. 113 (1959), 381[APS].
  31. R. Karplus, C. M. Sommerfield and E. H. Wichmann, Phys. Rev. 114 (1959), 376[APS].
  32. K. Hiida and N. Nakanishi, Prog. Theor. Phys. 22 (1959), 863[PTP].
  33. J. Otokozawa, Prog. Theor. Phys. 25 (1961), 277[PTP].
  34. M. Gell-Mann, M. L. Goldberger and W. E. Thirring, Phys. Rev. 95 (1954), 1612[APS].
  35. M. L. Goldberger, Phys. Rev. 97 (1955), 508[APS]; ibid. 99 (1955), 979[APS].
  36. N. N. Bogoliubov, B. V. Medvedev and M. K. Polivanov. Problems of the Theory of Dispersion Relations (1957, Princeton), unpublished.
  37. N. A. Chernikov, A. A. Logunov and I. T. Todorov, preprint.
  38. Y. Nambu, Phys. Rev. 98 (1955), 803[APS].
  39. Y. Nambu, Phys. Rev. 100 (1955), 394[APS].
  40. J. Schwinger, Proceedings of the 7th Conference on High Energy Nuclear Physics at Rochester (1957).
  41. G. Källén and A. Wightman, Mat. Fys. Skr. Dan. Vid. Selsk. 1 (1958) No. 6.
  42. R. Jost and H. Lehmann, Nuovo Cim. 5 (1957), 1598.
  43. F. J. Dyson, Phys. Rev. 110 (1958), 1460[APS].
  44. F. J. Dyson, Phys. Rev. 111 (1958), 1717[APS].
  45. S. Deser, W. Gilbert and E. C. T. Sudarshan, Phys. Rev. 115 (1959), 731[APS].
  46. M. Ida, Prog. Theor. Phys. 23 (1960), 1151[PTP].
  47. F. J. Dyson, Phys. Rev. 117 (1960), 1616[APS].
  48. A. Minguzzi and R. F. Streater, Phys. Rev. 119 (1960), 1127[APS].
  49. R. F. Streater, Proc. R. Soc. (London) A 256 (1960), 39.
    R. F. Streater, J. Math. Phys. 1 (1960), 231[AIP Scitation].
    R. F. Streater, Nuovo Cim. 15 (1960), 937.
  50. S. Mandelstam, Phys. Rev. 115 (1959), 1741[APS]; ibid. 115 (1959), 1752[APS].
  51. T. W. B. Kibble, Phys. Rev. 117 (1960), 1159[APS].
    see also J. Tarski. J. Math. Phys. 1 (1960), 149[CrossRef].
  52. J. Bowcock and A. Martin, Nuovo. Cim. 14 (1959), 516.
    R. Blankenbecler, M. L. Goldberger, N. N. Khuri and S. B. Treiman, Ann. of Phys. 10 (1960), 62[CrossRef].
    A. Klein, J. Math. Phys. 1 (1960), 41[CrossRef].
  53. G. Wanders, Nuovo. Cim 17 (1960), 535.
  54. R. J. Eden, Phys. Rev. Lett. 5 (1960), 213[APS].
    R. J. Eden, Phys. Rev. 120 (1960), 1514[APS]; ibid. 121 (1961), 1567[APS].
  55. P. V. Landshoff, J. C. Polkinghorne and J. C. Taylor, Nuovo Cim. 19 (1961), 939.
    R. J. Eden, P. V. Landshoff, J. C. Polkinghorne and J. C. Taylor, Phys. Rev. 122 (1961), 307[APS].
  56. N. Nakanishi, Prog. Theor. Phys. 24 (1960), 1275[PTP]; ibid. 25 (1961), 155[PTP].
  57. D. Gale, Pacific J. Math. 7 (1957), 1073.
  58. G. Konisi and K. Yamamoto, Prog. Theor. Phys. 25 (1961), 461[PTP].
  59. K. Yamamoto, Prog. Theor. Phys. 25 (1961), 361[PTP].
  60. M. Sato, J. Facul. Sci. (Univ. of Tokyo), Sec. 1, Vol. 8, Part 1 (1959), 139; Part 2 (1960), 387.
  61. F. J. Dyson, Phys. Rev. 75 (1949), 1736[APS].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 26 No. 3 (1961) pp. 337-355 :
    Integral Representations for Scattering Amplitudes in Perturbation Theory
    Noboru Nakanishi
  2. Progress of Theoretical Physics Vol. 26 No. 6 (1961) pp. 927-941 :
    Integral Representations for Scattering Amplitudes in Perturbation Theory. II
    Noboru Nakanishi
  3. Progress of Theoretical Physics Vol. 32 No. 6 (1964) pp. 950-955 :
    Some Theorems on the U-Functions of Parametrized Feynman Amplitudes
    Yutze Chow and Daniel J. Kleitman
  4. Progress of Theoretical Physics Vol. 40 No. 4 (1968) pp. 864-892 :
    Position-Space Analytic Functions Dual to the Feynman Integrals and Their Mass-Superpositions
    Masatsugu Minami
  5. 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
  6. Progress of Theoretical Physics Vol. 44 No. 5 (1970) pp. 1317-1339 :
    The Reggeization of the Bethe-Salpeter Scattering Amplitudes
    Hideki Matsumoto
  7. Progress of Theoretical Physics Vol. 52 No. 1 (1974) pp. 304-312 :
    Integrability and Regularization in Local Field Theory
    Kunio Yamamoto
  8. Progress of Theoretical Physics Vol. 58 No. 6 (1977) pp. 1935-1946 :
    Wave Function and Wave Equation on a Null-Plane
    Haruichi Yabuki

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

Copyright © Progress of Theoretical Physics 2013 All rights reserved.