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Prog. Theor. Phys. Vol. 39 No. 6 (1968) pp. 1585-1597

Multiple Poles in the Scattering Green's Function and the Lightlike Limit of the Bethe-Salpeter Amplitude

Noboru Nakanishi

Research Institute for Mathematical Sciences, Kyoto University, Kyoto

(Received January 23, 1968)

Abstract:

It is investigated how the Bethe-Salpeter amplitudes behave, when the bound-state four-momentum tends to a lightlike vector, in the ladder model in which two scalar particles exchange scalar particles having mass µ. For µ≠0, it is inferred that the scattering Green's function has multiple poles at s=0, where s stands for the invariant total energy squared, by proving that certain Bethe-Salpeter amplitudes are missing at s=0 in the equal-mass case. Some evidences of the existence of multiple poles are pointed out also in the unequal-mass case with µ≠0.

URL : http://ptp.ipap.jp/link?PTP/39/1585/
DOI : 10.1143/PTP.39.1585

[ Full Text PDF : FREE ACCESS (676K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 40 No. 2 (1968) pp. 412-419 :

   Spectra of Massless and Zero Energy-Momentum Solutions of the Bethe-Salpeter Equation

   Seiichi Naitô

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. 2 (1969) pp. 500-515 :

   Multiple Poles in the Off-Shell Scattering Amplitude

   Seichi Naito

4. Progress of Theoretical Physics Vol. 41 No. 2 (1969) pp. 516-526 :

   Daughter Trajectories, the Freedman-Wang Cancellation and Multiple Regge Poles

   Noboru Nakanishi

5. Progress of Theoretical Physics Vol. 41 No. 3 (1969) pp. 780-787 :

   Coinciding Simple Poles in the Scattering Green's Function

   Noboru Nakanishi

6. Progress of Theoretical Physics Vol. 42 No. 2 (1969) pp. 402-407 :

   Reality of the Eigenvalues of the Bethe-Salpeter Equation

   Seichi Naito and Noboru Nakanishi

7. 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

8. Progress of Theoretical Physics Vol. 43 No. 3 (1970) pp. 808-829 :

   Some Mathematical Aspects of Multiple Poles in the Off-Shell Scattering Amplitude

   Masakuni Ida

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