Non-crystallographic reduction of generalized Calogero–Moser models

Andreas Fring, Christian Korff
2006 Journal of Physics A: Mathematical and General  
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
more » ... odels how the corresponding classical equations of motion can be derived from a Lie algebraic Lax pair based on the larger, crystallographic Coxeter group.
doi:10.1088/0305-4470/39/5/007 fatcat:hmygjh3p6fa3bdgmy42bke636y