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Prog. Theor. Phys. Vol. 41 No. 1 (1969) pp. 233-251

General Theory of Multiple Poles and Coinciding Simple Poles

Noboru Nakanishi

Research Institute for Mathematical Sciences, Kyoto University, Kyoto

(Received July 19, 1968)

Abstract:

It is investigated in the general framework of the Bethe-Salpeter formalism how multiple poles of the scattering Green's function are synthesized out of coinciding simple poles. A necessary and sufficient condition for the existence of the leading multiple pole is obtained and applied to some concrete examples. The residues of multiple poles and the corresponding generalized Bethe-Salpeter amplitudes are expressed in terms of the residues of simple poles and the ordinary Bethe-Salpeter amplitudes, respectively. Some comments are made on the conspiracy problem from the standpoint of the multiple-pole theory.

URL : http://ptp.ipap.jp/link?PTP/41/233/
DOI : 10.1143/PTP.41.233

[ Full Text PDF : FREE ACCESS (905K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 41 No. 2 (1969) pp. 500-515 :

   Multiple Poles in the Off-Shell Scattering Amplitude

   Seichi Naito

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

   Daughter Trajectories, the Freedman-Wang Cancellation and Multiple Regge 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. 4 (1969) pp. 1094-1108 :

   Unequal-Mass Conspiracy for Arbitrary Spins

   Noboru Nakanishi and Noriaki Seto

5. Progress of Theoretical Physics Vol. 41 No. 5 (1969) pp. 1328-1339 :

   Cancellation of the Singularities of the Backward Unequal-Mass Regge-Pole Terms

   Masatsugu Minami

6. 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

7. 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

8. Progress of Theoretical Physics Vol. 55 No. 2 (1976) pp. 604-609 :

   Remarks on the Bethe-Salpeter Equation in a Model with Dynamical Higgs Mechanism

   Noboru Nakanishi and Kan-ichi Yokoyama

9. Progress of Theoretical Physics Vol. 56 No. 3 (1976) pp. 972-980 :

   Vector Field with a Bare Mass and the Higgs Mechanism

   Masahiko Konoue and Noboru Nakanishi

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

    Review of the Wick-Cutkosky Model

    Noboru Nakanishi

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