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Non-crystallographic reduction of generalized Calogero-Moser models

Andreas Fring·Christian Korff
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Abstract

We apply a recently introduced reduction procedure based on the embedding of non-crystallographic Coxeter groups into crystallographic ones to Calogero-Moser systems. For rational potentials the familiar generalized Calogero Hamiltonian is recovered. For the Hamiltonians of trigonometric, hyperbolic and elliptic type, we obtain novel integrable dynamical systems with a second potential term which is rescaled by the golden ratio. We explicitly show for the simplest of these non-crystallographic models how the corresponding classical equations of motion can be derived from a Lie algebraic Lax pair based on the larger, crystallographic Coxeter group.

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Andreas Fring, Christian Korff. 2005-09-20. Non-crystallographic reduction of generalized Calogero-Moser models. https://doi.org/10.1088/0305-4470%2F39%2F5%2F007

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