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Prog. Theor. Phys. Vol. 27 No. 1 (1962) pp. 133-138
Some Analytic Properties of Absorptive Part of Scattering Amplitude
Kunio Yamamoto
Department of Physics, Osaka University, Osaka
(Received August 28, 1961)
Abstract:
By using the graphical interpretation of Dyson's integral representation of the causal commutator, it is shown that the absorptive part of the scattering amplitude has two singularities. One has the close connection with the maximum momentum transfer below which the dispersion relation holds, and the other has the close connection with the anomalous threshold. The main purpose of this paper is to discuss the latter singularity. It is found that, so far as the latter singularity is concerned, the scattering amplitude and the vertex function are the same situation in all respects. For example, if the dispersion relation holds and the threshold does not depend on the momentum transfer, even in the case where the anomalous threshold appears, the threshold of the dispersion relation of the scattering amplitude cannot be lower than that of the corresponding vertex function.
URL :
http://ptp.ipap.jp/link?PTP/27/133/
DOI : 10.1143/PTP.27.133
References:
- K. Yamamoto, Prog. Theor. Phys. 25 (1961), 361[PTP].
- G. Konisi and K. Yamamoto, Prog. Theor. Phys. 25 (1961), 461[PTP].
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F. J. Dyson, Phys. Rev. 110 (1958), 1460[APS].
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H. J. Bremermann, R. Oehme and J. G. Taylor, Phys. Rev. 109 (1958), 2178[APS].
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R. Oehme and J. G. Taylor, Phys. Rev. 113 (1959), 371[APS].
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R. Karplus, C. M. Sommerfield and E. H. Wichmann, Phys. Rev. 111 (1958), 1187[APS];
ibid. 114 (1959), 376[APS].
- K. Yamamoto, Prog. Theor. Phys. 25 (1961), 1056[PTP].
- N. Nakanishi, Prog. Theor. Phys. 21 (1959), 135[PTP].
Citing Article(s) :
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Progress of Theoretical Physics Vol. 28 No. 6 (1962) pp. 1080-1099
:
-
Baryon Number Conservation and the Jost-Lehmann-Dyson Representatin
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Gaku Konisi and Kunio Yamamoto
