Quick Search:
Author: Title/Abstract: Vol./No: Page:

Prog. Theor. Phys. Vol. 34 No. 1 (1965) pp. 92-115

[ Full Text PDF : FREE ACCESS (1419K) ]

Green's Funtion Approach and Its Equivalence with the Ordinary N/D Method

Masakuni Ida

Department of Physics, Kyoto University, Kyoto

(Received February 22, 1965)

Abstract:

Green's function approach to the scattering of two particles in a channel with a one-particle intermediate state is investigated in detail under the elastic approximation, with due attention to propagator zeros. In relation to the asymptotic behavior of the spectral function in the Lehmann representation of the propagator, particles are classified into four types; super-elementary, elementary, intermediate and composite. It is shown that the present approach is equivalent to the ordinary N/D method. Criticism to some earlier works is also given.


URL : http://ptp.ipap.jp/link?PTP/34/92/
DOI : 10.1143/PTP.34.92

[ Full Text PDF : FREE ACCESS (1419K) ] Citation:


References:

  1. See, for instance, F. Zachariasen and C. Zemach, Phys. Rev. 128 (1962), 849[APS].
  2. G. F. Chew and S. Mandelstam, Phys. Rev. 119 (1960), 467[APS].
  3. G. F. Chew and S. C. Frautschi, Phys. Rev. Lett. 7 (1961), 394[APS].
  4. B. Jouvet, Nuovo Cim. 5 (1957), 1.
    J. Houard and B. Jouvet, Nuovo Cim. 18 (1960), 466.
    D. Lurié and A. J. Macfarlane, Phys. Rev. 136 (1964), B816[APS].
  5. A. Salam, Nuovo Cim. 25 (1962), 224.
    J. S. Dowker, Nuovo Cim. 29 (1963), 551; ibid. 33 (1964), 110.
  6. S. Weinberg, Phys. Rev. 130 (1963), 776[APS].
  7. J. G. Taylor, Nuovo Cim. Suppl. 1 (1963), 857.
    See the sixth of a series of his papers.
  8. A traditional approach to the concept of elementarity in terms of bare states will be found in:
    H. Ezawa, T. Muta and H. Umezawa, Prog. Theor. Phys. 29 (1963), 877[PTP].
  9. M. T. Vaughn, R. Aaron and R. D. Amado, Phys. Rev. 124 (1961), 1258[APS].
  10. R. Acharya, Nuovo Cim. 24 (1962), 870.
    J. S. Dowker, Nuovo Cim. 25 (1962), 1135.
    M. L. Whippman and I. S. Gerstein, Phys. Rev. 134 (1964), B1123[APS].
  11. S. Saito and T. Akiba, Prog. Theor. Phys. 33 (1965), 307[PTP].
  12. R. M. Rockmore, Phys. Rev. 132 (1963), 878[APS].
  13. M. Ida, Phys. Rev. 135 (1964), B499[APS].
  14. B. W. Lee, K. T. Mahanthappa, I. S. Gerstein and M. L. Whippman, Ann. of Phys. 28 (1964), 466[CrossRef].
  15. M. Uehara, Prog. Theor. Phys. 32 (1964), 306[PTP].
  16. C. J. Goebel and B. Sakita, Phys. Rev. Lett. 11 (1963), 293[APS].
  17. B. V. Geshkenbein and B. L. Ioffe, Phys. Rev. Lett. 11 (1963), 55[APS].
  18. M. Ida, Phys. Rev. 136 (1964), B1767[APS].
  19. H. Lehmann, Nuovo Cim. 11 (1954), 342.
  20. R. Blankenbecler, M. L. Goldberger, N. N. Khuri and S. B. Treiman, Ann. of Phys. 10 (1960), 62[CrossRef].
  21. L. Castillejo, R. H. Dalitz and F. J. Dyson, Phys. Rev. 101 (1956), 453[APS].
  22. G. Källén, Proceedings of the CERN Symposium on High-Energy Accelerators and Pion Physics (CERN, Geneva, 1956), Vol. 2, p. 187.
    See also K. Symanzik, Nuovo Cim. 11 (1959), 269;
    M. Gell-Mann and F. Zachariasen, Phys. Rev. 123 (1961), 1065[APS].
  23. F. Zachariasen, Phys. Rev. 121 (1961), 1851[APS].
  24. N. Levinson, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 25 (1949), No. 9.
  25. M. Ida, Prog. Theor. Phys. 21 (1959), 625[PTP].
  26. See also S. D. Drell, A. C. Finn and A. C. Hearn, Phys. Rev. 136 (1964), B1439[APS].
  27. H. Lehmann, K. Symanzik and W. Zimmermann, Nuovo Cim. 2 (1955), 425.
    See also I.
  28. H. Miyazawa and H. Sugawara, Prog. Theor. Phys. 29 (1963), 735[PTP].
  29. P. Federbush, M. L. Goldberger and S. B. Treiman, Phys. Rev. 112 (1958), 642[APS].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 34 No. 4 (1965) pp. 636-652 :
    Models of the π Meson and Its Compositeness
    Kenji Hayashi, Masakuni Ida, Toshikatsu Saegusa, Takeshi Shirafuji and Masayuki Uehara
  2. Progress of Theoretical Physics Vol. 34 No. 5 (1965) pp. 825-832 :
    Many-Pole Amplitudes and Elementarity. I
    Kisei Kinoshita and Haruichi Yabuki
  3. Progress of Theoretical Physics Vol. 34 No. 6 (1965) pp. 981-989 :
    Many-Pole Amplitudes and Elementarity. II
    Kisei Kinoshita and Haruichi Yabuki
  4. Progress of Theoretical Physics Vol. 34 No. 6 (1965) pp. 990-999 :
    Properties of Noncomposite Particles
    Masakuni Ida
  5. Progress of Theoretical Physics Vol. 35 No. 1 (1966) pp. 104-116 :
    A General Effective-Range Formula and the Compositeness of the Deuteron
    Masakuni Ida
  6. Progress of Theoretical Physics Vol. 35 No. 2 (1966) pp. 337-339 :
    A Model of Pseudoscalar Mesons with the Z3 = 0
    Kenji Hayashi and Takeshi Shirafuji
  7. Progress of Theoretical Physics Vol. 35 No. 3 (1966) pp. 452-462 :
    Vertex Zeros and Levinson's Theorem
    Koichi Hayashi
  8. Progress of Theoretical Physics Vol. 35 No. 4 (1966) pp. 692-704 :
    N/D Methods for Multichannel Scattering
    Masakuni Ida
  9. Progress of Theoretical Physics Vol. 35 No. 5 (1966) pp. 889-896 :
    A Remark on the Condition, Z3 = 0
    Haruichi Yabuki
  10. Progress of Theoretical Physics Vol. 35 No. 5 (1966) pp. 962-964 :
    The Vertex Function and Renormalization Constant Z1
    Reijiro Kubo
  11. Progress of Theoretical Physics Vol. 35 No. 5 (1966) pp. 964-965 :
    Hidden Channels and Elementarity
    Kisei Kinoshita
  12. Progress of Theoretical Physics Vol. 35 No. 6 (1966) pp. 1043-1050 :
    C, P and T Invariances and the Bootstrap Hypothesis
    Naoki Tokuda
  13. Progress of Theoretical Physics Vol. 35 No. 6 (1966) pp. 1088-1098 :
    Compositeness Conditions and the Indefinite Nature of the Self-Mass
    Haruichi Yabuki
  14. Progress of Theoretical Physics Vol. 36 No. 1 (1966) pp. 138-147 :
    Multichannel Scattering and Equivalence between Four-Fermion and Yukawa Coupling
    Haruichi Yabuki
  15. Progress of Theoretical Physics Vol. 36 No. 2 (1966) pp. 380-393 :
    Behaviour of Masses and Coupling Constants in Two Processes Involving Vanishing Z3
    Kisei Kinoshita
  16. Progress of Theoretical Physics Vol. 36 No. 4 (1966) pp. 781-798 :
    Classification of an Unstable Particle and Its Propagator
    Masayuki Uehara
  17. 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
  18. Progress of Theoretical Physics Vol. 37 No. 5 (1967) pp. 1003-1028 :
    Composite Particle and Vertex Function in the Nonrelativistic Off-Shell Theory
    Nobuhiko Mishima and Miwae Yamazaki
  19. Progress of Theoretical Physics Vol. 37 No. 5 (1967) pp. 1034-1036 :
    A Compositeness Criterion for the Target Particles
    Yasuo Matsumoto
  20. Progress of Theoretical Physics Vol. 37 No. 6 (1967) pp. 1291-1303 :
    Bootstrap Conditions in a Model Field Theory
    Taizo Muta
  21. Progress of Theoretical Physics Vol. 38 No. 1 (1967) pp. 246-260 :
    Compositeness Condition and Propagator
    Takeshi Shirafuji
  22. Progress of Theoretical Physics Vol. 38 No. 2 (1967) pp. 460-471 :
    Goldberger-Treiman Relation and the Elementarity of the Pion
    Kisei Kinoshita
  23. Progress of Theoretical Physics Vol. 38 No. 3 (1967) pp. 705-714 :
    The Double N/D Method
    Kisei Kinoshita
  24. Progress of Theoretical Physics Vol. 38 No. 6 (1967) pp. 1347-1360 :
    A Model of the Nucleon and the P11 Resonance as a Bound State of a Hidden Channel
    Masayuki Uehara
  25. Progress of Theoretical Physics Vol. 39 No. 1 (1968) pp. 108-117 :
    Effect of Hidden Channels on Low-Lying Channels
    Kisei Kinoshita, Yukiko Kinoshita and Nobuyuki Murai
  26. Progress of Theoretical Physics Vol. 39 No. 1 (1968) pp. 166-181 :
    Bootstrap Conditions in S-Matrix Theory
    Seiya Aramaki, Seiji Fukuzumi and Masatosi Ito
  27. Progress of Theoretical Physics Vol. 40 No. 5 (1968) pp. 1060-1067 :
    Multi-Resonance Structure in the P11 State of πN Scattering
    Masayuki Uehara
  28. Progress of Theoretical Physics Vol. 48 No. 6 (1972) pp. 1986-2007 :
    Exact Upper Bound for Pion-Nucleon Coupling Constant
    Susumu Okubo
  29. Progress of Theoretical Physics Vol. 55 No. 1 (1976) pp. 211-228 :
    Whole-Region Description of Inclusive Spectra and Composite Structure of Hadrons
    Kisei Kinoshita, Yukio Kinoshita and Yasuo Myozyo
  30. Progress of Theoretical Physics Vol. 55 No. 5 (1976) pp. 1526-1536 :
    Z3δµ2 = 0 Condition and the HNZ Construction
    Shigeru Sasabe
  31. Progress of Theoretical Physics Vol. 74 No. 1 (1985) pp. 178-181 :
    The Enhancement of the Δ(1232) Width
    Masayuki Uehara, Ichio Fukui and Hiroki Kondo