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, which are 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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Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 2, pp. 341–347, May, 1993.
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Olshanetsky, M.A. Scattering of clusters in quantum calogero model. Theor Math Phys 95, 626–631 (1993). https://doi.org/10.1007/BF01017147
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DOI: https://doi.org/10.1007/BF01017147