Non-crystallographic reduction of generalized Calogero-Moser models

Details Non-crystallographic reduction of generalized Calogero-Moser models Non-crystallographic reduction of generalized Calogero-Moser models

2005-09-20

arxiv.org/abs/hep-th/0509152v1

J.Phys. A39 (2006) 1115-1132

Physics

High Energy Physics

High Energy Physics - Theory

21 pages

Scientific paper

10.1088/0305-4470/39/5/007

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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