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Prog. Theor. Phys. Vol. 27 No. 2 (1962) pp. 396-403

[ Full Text PDF : FREE ACCESS (466K) ]

Continuation of S-Matrix into Second Riemann Sheet

Takesi Ogimoto

Department of Physics, Osaka University, Osaka

(Received September 28, 1961)

Abstract:

In the framework of relativistic dispersion theory it is shown that the S-matrix continued into the second Riemann sheet is just the inverse of the one on the first Riemann sheet. This formula is used for deriving a dispersion-like relation between the real and imaginary parts of the scattering phase shift and also the product expansion for the S-matrix. It is noted that these results are generalizations of van Kampen's formulae in the theory of non-relativistic potential scattering to those in the relativistic field theory. The so-called Castillejo-Dalitz-Dyson ambiguity is discussed on the basis of our S-matrix. Relations connecting the sum of the oscillator strengths with scattering lengths are also derived in generalized forms.


URL : http://ptp.ipap.jp/link?PTP/27/396/
DOI : 10.1143/PTP.27.396

[ Full Text PDF : FREE ACCESS (466K) ] Citation:

References:

  1. N. G. van Kampen, Phys. Rev. 89 (1953), 1072[APS]; ibid. 91 (1953), 1267[APS].
  2. J. Gunson and J. G. Taylor, Phys. Rev. 119 (1960), 1121[APS].
    R. Oehme, Phys. Rev. 121 (1961), 1840[APS].
    R. Blankenbecler, M. L. Goldberger, S. W. MacDowell and S. B. Treiman, Phys. Rev. 123 (1961), 692[APS].
    W. Zimmermann, Nuovo Cim. 21 (1961), 249.
  3. L. Castillejo, R. H. Dalitz and F. J. Dyson, Phys. Rev. 101 (1956), 453[APS].
  4. This analytic property of the partial wave amplitude for the π-π scattering as well as the N-N scattering has now been proved by K. Yamamoto in all orders of perturbation theory:
    K. Yamamoto, Prog. Theor. Phys. 26 (1961), 1014[PTP].
    See also J. G. Taylor, Nuovo Cim. 22 (1961), 92.
    N. Nakanishi, Prog. Theor. Phys. 26 (1961), 337[PTP].
  5. S. Mandelstam, Phys. Rev. 112 (1958), 1344[APS].
  6. The same idea also is obtained by van Dam (private communication).

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 29 No. 1 (1963) pp. 71-86 :
    A Classification of Resonances
    Yasunori Fujii
  2. Progress of Theoretical Physics Vol. 29 No. 1 (1963) pp. 87-96 :
    Use of the Generalized Jost Function in Quantum Field Theory
    Takeshi Kanki
  3. Progress of Theoretical Physics Vol. 29 No. 1 (1963) pp. 97-103 :
    Restriction on the Coupling Constant from Analyticity and Unitarity of the S-Matrix
    Takeshi Kanki and Takesi Ogimoto
  4. Progress of Theoretical Physics Vol. 29 No. 2 (1963) pp. 322-324 :
    N/D Method and Inverse-Amplitude Method
    Takeshi Kanki
  5. Progress of Theoretical Physics Vol. 31 No. 5 (1964) pp. 916-920 :
    Construction of the Jost Function Including Inelastic Processes
    Takesi Ogimoto

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