---

Prog. Theor. Phys. Vol. 55 No. 5 (1976) pp. 1591-1605

Solutions of the Spinor-Spinor Bethe-Salpeter Equation in the Scalar-Vector Sector

Kiyoshi Higashijima

Department of Physics, University of Tokyo, Tokyo 113

(Received September 19, 1975; Revised December 26, 1975)

Abstract:

The scalar-vector sector parts of the spinor-spinor Bethe-Salpeter equation for the vanishing total four-momentum are investigated in detail. By means of the Hankel transformation, they are reduced to a second order differential equation. By solving it, general features of solutions for various cases are discussed, and new solutions are found.

URL : http://ptp.ipap.jp/link?PTP/55/1591/
DOI : 10.1143/PTP.55.1591

[ Full Text PDF : FREE ACCESS (920K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

---

References:

1. E. E. Salpeter and H. A. Bethe, Phys. Rev. 84 (1951), 1232[APS].
   See also the excellent review paper 2) and references therein.
2. N. Nakanishi, Prog. Theor. Phys. Suppl. No. 43 (1969), 1[PTP].
3. J. Goldstein, Phys. Rev. 91 (1953), 1516[APS].
   See also the Appendix of Ref. 4).
4. W. Kummer, Nuovo Cim. 31 (1964), 219 [Errata; 34 (1964), 1840].
5. For example, N. Nakanishi, J. Math. Phys. 12 (1971), 1578[CrossRef];
   H. Ito, Prog. Theor. Phys. 43 (1970), 1035[PTP].
   See also Ref. 7).
6. A. Bastai, L. Bertocchi, G. Furlan and M. Tonin, Nuovo Cim. 30 (1964), 1532.
7. R. F. Keam, J. Math. Phys. 12 (1971), 515[CrossRef].
8. A. Bastai, L. Bertocchi, S. Fubini, G. Furlan and M. Tonin, Nuovo Cim. 30 (1963), 1512.
   See also Ref. 6).
9. C. Snow, `Hypergeometric and Legendre functions wth applications to integral equations of potential theory.' Applied Mathematics Series 19 (National Bureau of Standards. 1952).
   See also A. Erdelyi, W. Magnus, H. Oberhettinger and F. Tricomi, Higher Transcendental Functions (McGraw-Hill Book Company, Inc., New York, 1955), Vol. III.
10. F. L. Ince, Ordinary differential equations (Dover Publications, Inc.), Chapter XVIII.
    See also A. Erdelyi et al., Higher Transcendental Functions, Vol. I.

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 56 No. 3 (1976) pp. 908-918 :

   Exact Solutions of the Spinor-Spinor Bethe-Salpeter Equation and Their Gauge Dependence

   Akitoshi Nishimura and Kiyoshi Higashijima

2. Progress of Theoretical Physics Vol. 58 No. 5 (1977) pp. 1585-1593 :

   Spinor-Spinor Bethe-Salpeter Equation

   Ichio Fukui, Noriaki Setô and Toshihiro Yoshida

3. Progress of Theoretical Physics Vol. 64 No. 1 (1980) pp. 300-309 :

   Spectral Properties of the Spinor-Spinor Bethe-Salpeter Equation

   Noriaki Setô

4. Progress of Theoretical Physics Supplement No.95 (1988) pp. 25-45 :

   Review of the Spinor-Spinor Bethe-Salpeter Equation

   Noriaki Setô

---

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

Copyright © Progress of Theoretical Physics 2013 All rights reserved.