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Prog. Theor. Phys. 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

Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606

(Received June 16, 1972)

Abstract:

In the equal-mass or unequal-mass Wick-Cutkosky model, two apparently different sets of solutions are known to be obtained by the stereographic-projection method. The equivalence between them is explicitly demonstrated by proving a remarkable integral formula for the Cutkosky function. Some instructive discussions are made on the normalization integral of the solution.

URL : http://ptp.ipap.jp/link?PTP/48/2066/
DOI : 10.1143/PTP.48.2066

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References:

1. N. Nakanishi, Prog. Theor. Phys. Suppl. No. 43 (1969), 1[PTP].
2. R. E. Cutkosky, Phys. Rev. 96 (1954), 1135[APS].
3. K. Seto, Prog. Theor. Phys. 39 (1968), 453[PTP]; ibid. 41 (1969), 1340[PTP].
4. R. Delbourgo, A. Salam and J. Strathdee, Nuovo Cim. A 50 (1967), 193.
5. J. M. Golden, Nucl. Phys. B 23 (1970), 19[CrossRef].
6. H. S. Green, Nuovo Cim. 5 (1957), 866.
7. N. Nakanishi, Phys. Rev. 147 (1966), 1153[APS].
8. N. Nakanishi, Graph Theory and Feynman Integrals (Gordon and Breach, New York, 1971), Appendix B-2.
9. N. Nakanishi, Prog. Theor. Phys. 38 (1967), 226[PTP].
10. N. Nakanishi, Phys. Rev. 138 (1965), B1182[APS].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 49 No. 3 (1973) pp. 1014-1026 :

   An Integral Formula for the Unequal-Mass Wick-Cutkosky Model of the Bethe-Salpeter Equation

   Noriaki Setô

2. Progress of Theoretical Physics Supplement No.95 (1988) pp. 1-24 :

   Review of the Wick-Cutkosky Model

   Noboru Nakanishi

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