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Prog. Theor. Phys. Vol. 39 No. 5 (1968) pp. 1319-1325
Two-Dimensional Euclidean Group and the Partial-Wave Expansion. I
Tadashi Miyazaki
Department of Physics, University of Tokyo, Tokyo
(Received December 25, 1967)
Abstract:
When we decompose the invariant amplitude f(s, t) into the partial-wave scattering amplitudes for fixed t, we must consider four different cases according to the values of t. The amplitude f(s, t) is considered as a function over a little group. For t=0, two cases occur; we treat the case where the little group is two-dimensional Euclidean group E2. Taking f(s, t=0) as a function over E2, we get the partial-wave expansion according to the unitary irreducible representations of E2 and can pick out the Regge behavior from this expansion. We find that this group-theoretical method is essentially the “eikonal” approximation representation.
URL :
http://ptp.ipap.jp/link?PTP/39/1319/
DOI : 10.1143/PTP.39.1319
References:
- M. Toller, Nuovo Cim. 37 (1965), 631.
L. Sertorio and M. Toller, Nuovo Cim. 33 (1964), 413.
- M. Toller, Nuovo Cim. 53 (1968), 671.
- S. Itô, Nagoya Math. J., Nagoya University, 4 (1952), 1.
- S. Itô, Nagoya Math. J., Nagoya University, 5 (1953), 79.
- I. Gelfand and M. Neumark, Doklady Akad. Nauk SSSR, 55 (1947), 567.
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R. Blankenbecler and M. L. Goldberger, Phys. Rev. 126 (1962), 766[APS].
- For the representations of the generalized Lorentz groups, see the next marvellous works.
T. Shintani, Proc. Jpn. Acad 43 (1967), 1.
T. Shintani, Lectures at the Research Inst. Math. Sci., Kyoto University.
He has obtained the unitary irreducible representations of the generalized Lorentz groups SO(p, q) (to be published).
Citing Article(s) :
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Progress of Theoretical Physics Vol. 40 No. 3 (1968) pp. 620-627
:
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Normalization of the Degenerate B-S Amplitudes
-
Jiro Arafune
