1207.3657 (C. Klimcik)

Totally classical Calogero model    [PDF]

C. Klimcik

We introduce a concept of a classical Lax observable L which is a function on the direct product of two phase spaces A and B such that the B-symplectic averages of all powers of L are mutually A-Poisson commuting. The classical integrable system on A for which those symplectic averages are the action variables is referred to as totally classical. We construct a simple nontrivial example of the totally classical integrable system with the phase space B being the standard symplectic sphere. The Lax observable of this system depends very simply on the spherical angles and upon replacing the sphere B by the fuzzy sphere it becomes the Lax matrix of the standard rational Calogero model.

View original: http://arxiv.org/abs/1207.3657