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 TMF, 1993, Volume 95, Number 2, Pages 341–347 (Mi tmf1471)

Scattering of clusters in quantum calogero model

M. A. Olshanetsky

Abstract: It is well known that scattering of particles in the Calogero model, which recently drew attention in connection with $c=1$ strings and integrable models in statistical mechanics, is reduced to two-particle collisions. It follows from Harish-Chandra and Gindikin–Karpelevich results, related to the harmonic analysis on simple Lie groups. Unfortunately their formulae don't work if particles form clusters in the asymptotics. We reformulate their results in a form which allows to apply them to this situation. The scattering of clusters is also factorizible, but depends on structures of constituents. In conclusion we discuss a similar problem in the deformed Calogero model related to quantum groups, which describes also interactions of excited states in the XXZ-model.

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English version:
Theoretical and Mathematical Physics, 1993, 95:2, 626–631

Bibliographic databases:

Citation: M. A. Olshanetsky, “Scattering of clusters in quantum calogero model”, TMF, 95:2 (1993), 341–347; Theoret. and Math. Phys., 95:2 (1993), 626–631

Citation in format AMSBIB
\Bibitem{Ols93} \by M.~A.~Olshanetsky \paper Scattering of clusters in quantum calogero model \jour TMF \yr 1993 \vol 95 \issue 2 \pages 341--347 \mathnet{http://mi.mathnet.ru/tmf1471} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1243259} \zmath{https://zbmath.org/?q=an:0852.35136} \transl \jour Theoret. and Math. Phys. \yr 1993 \vol 95 \issue 2 \pages 626--631 \crossref{https://doi.org/10.1007/BF01017147} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993ML10100016}