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Prog. Theor. Phys. Vol. 39 No. 2 (1968) pp. 453-459

[ Full Text PDF : FREE ACCESS (390K) ]

On the Normalization of the Bethe-Salpeter Wave Function in the Unequal-Mass Case by Means of the Stereographic Projection Method

Kenji Seto

Department of Physics, Faculty of Science, Hokkaido University, Sapporo

(Received August 14, 1967)

Abstract:

The stereographic projection method, which was introduced by Cutkosky in solving the Bethe-Salpeter equation in the equal-mass case, is applied to solving the B-S equation in the case where the constituent particles have different masses. The solution thus obtained is expressed in a spectral representation, which enables us to calculate the norm of the B-S amplitude for arbitrary n-l-1 where n and l are the principal and the angular momentum quantum number. The solution coincides with that obtained by Nakanishi for n-l-1=0.1 and 2.


URL : http://ptp.ipap.jp/link?PTP/39/453/
DOI : 10.1143/PTP.39.453

[ Full Text PDF : FREE ACCESS (390K) ] Citation:

See Also:

References:

  1. N. Nakanishi, Phys. Rev. 147 (1966), 1153[APS].
  2. G. C. Wick, Phys. Rev. 96 (1954), 1124[APS].
  3. R. E. Cutkosky, Phys. Rev. 96 (1954), 1135[APS].
  4. N. Nakanishi, Prog. Theor. Phys. 37 (1967), 618[PTP].
  5. N. Nakanishi, Prog. Theor. Phys. 38 (1967), 226[PTP].
  6. N. Nakanishi, Phys. Rev. 138 (1965), B1182[APS]; ibid. 139 (1965), B1401[APS].
  7. R. E. Cutkosky and M. Leon, Phys. Rev. 135 (1964), B1445[APS].
  8. D. Lurié, A. J. Macfarlane and Y. Takahashi, Phys. Rev. 140 (1965), B1091[APS].
  9. Y. Ohnuki and K. Watanabe, Prog. Theor. Phys. Suppl. Extra Number (1965), 416[PTP].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 40 No. 3 (1968) pp. 605-619 :
    Relativistic Regge Approach from the Bethe-Salpeter Equation
    Kenji Seto
  2. Progress of Theoretical Physics Vol. 41 No. 1 (1969) pp. 233-251 :
    General Theory of Multiple Poles and Coinciding Simple Poles
    Noboru Nakanishi
  3. Progress of Theoretical Physics Vol. 41 No. 3 (1969) pp. 780-787 :
    Coinciding Simple Poles in the Scattering Green's Function
    Noboru Nakanishi
  4. Progress of Theoretical Physics Vol. 41 No. 5 (1969) pp. 1340-1351 :
    On the Solutions of the Bethe-Salpeter Equation in the Unequal-Mass Wick-Cutkosky Model in the Moving System
    Kenji Seto
  5. Progress of Theoretical Physics Vol. 42 No. 6 (1969) pp. 1394-1417 :
    Generalized O(4) Harmonics and Bethe-Salpeter Equation for Spinor-Spinor Particle System
    Kenji Seto
  6. Progress of Theoretical Physics Vol. 43 No. 1 (1970) pp. 184-205 :
    An Attempt at a General Theory of the Bethe-Salpeter Equation
    Masakuni Ida
  7. Progress of Theoretical Physics Vol. 46 No. 3 (1971) pp. 909-937 :
    Regge Trajectories in the Wick-Cutkosky Model
    Nobuyuki Murai, Koichi Nakamura and Hiroshi Ezawa
  8. Progress of Theoretical Physics Vol. 48 No. 6 (1972) pp. 2066-2076 :
    On the Bethe-Salpeter Amplitudes Obtained by Means of the Stereographic Projection in the Wick-Cutkosky Model
    Noboru Nakanishi
  9. Progress of Theoretical Physics Vol. 53 No. 3 (1975) pp. 797-802 :
    On the Eigenvalues of the Wick-Cutkosky Model
    Fujio Tanaka and Noboru Nakanishi
  10. Progress of Theoretical Physics Vol. 114 No. 1 (2005) pp. 213-237 :
    General, Relativistic, Bound-State Solutions of a Spin-0 and Spin-1/2 Constituent Interacting via Scalar Electrodynamics
    G. B. Mainland
  11. Progress of Theoretical Physics Supplement No.95 (1988) pp. 1-24 :
    Review of the Wick-Cutkosky Model
    Noboru Nakanishi

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