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Prog. Theor. Phys. Vol. 47 No. 6 (1972) pp. 2015-2039

[ Full Text PDF : FREE ACCESS (1372K) ]

Theory of the Reactions of the Composite Particles

Shigeru Machida

Department of Physics, Kyoto University, Kyoto

(Received December 10, 1971)

Abstract:

Theory of the reactions of hadrons, assumed to be composed of urbaryons with the degree of freedom of the spatial motion as well as those of unitary spin and spin, is discussed. An integral equation is derived for the one-time Bethe-Salpeter (BS) amplitude, based on the observation that the knowledge of the BS amplitude with the same value of time variables for all constituent particles is sufficient to derive the S-matrix element and by introducing the modified interaction kernel. The equation is a Klein-Gordon type integral equation in the momentum space, whose interaction kernel is energy-dependent and nonlocal and is also shown to be complex normal in general. Dispersion relations for that kernel and properties of their eigenvalues are also discussed. Resonances are discussed on the basis of the expansion of the kernel and the resolvent by the eigenvalues and the eigenfunctions of the kernel. The S-matrix element is shown to obey a difference equation approximately. By generalizing this difference equation so as to satisfy the crossing symmetry and by solving the resulting simultaneous difference equations with a suitably chosen form of the eigenvalues, we obtain a generalization of the Veneziano or the Virasoro amplitude. The original Veneziano or Virasoro amplitude is obtained as a limit of the above function which corresponds to the case of the eigenvalues of the kernel being a linear function of the square of the total energy in the center-of-mass system.


URL : http://ptp.ipap.jp/link?PTP/47/2015/
DOI : 10.1143/PTP.47.2015

[ Full Text PDF : FREE ACCESS (1372K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 48 No. 1 (1972) pp. 267-271 :
    Possible Behaviour of Regge Trajectories in Veneziano-Like Representations
    Masanori Kobayashi
  2. Progress of Theoretical Physics Vol. 51 No. 4 (1974) pp. 1159-1171 :
    Relativistic Composite Model Consistent with the Bethe-Salpeter Equation, Approximate SU(6) Symmetry and Duality. I
    Shigeru Machida
  3. Progress of Theoretical Physics Vol. 54 No. 2 (1975) pp. 510-525 :
    Solutions of the Bethe-Salpeter Equation with Dual Interaction Kernel for Baryons and SU(6)⊗O(3)L Symmetry
    Shigeru Machida and Hisao Nakkagawa

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