Generalizations of Calogero Systems

Marijan Mileković, Stjepan Meljanac, Andjelo Samsarov

Kazuhiro Hikami, Miki Wadati

Joshua Feinberg

The relation between the Calogero model, namely, a system of N identical particles in one dimension with inverse-square interactions, and the three classical types of quantum-mechanical matrix models is well-known. In this talk I explore various generalized Calogero models and identify the quantum mechanical matrix model they correspond to at special values of their couplings. I also present and briefly discuss the collective field formulation of these generalized Calogero models.

Jialiang Dai

Abstract We present universal construction for the Calogero-Moser system with two types spins interaction of trigonometric potential based on the root system of semi-simple Lie algebra. In this formalism, we successfully build up the correct Lax pair as well as the R-matrix for this generalized Calogero-Moser models. Moreover using the property of root system, we make a concise explanation that in the quantized model, the R-matrix takes the same form as the classical one, which is the main new result of this paper.

Vincent Pasquier

Polychronakos, A P

We construct generalizations of the Calogero-Sutherland-Moser system by appropriately reducing a model involving many unitary matrices. The resulting systems consist of particles on the circle with internal degrees of freedom, coupled through modifications of the inverse-square potential. The coupling involves SU(M) non-invariant (anti)ferromagnetic interactions of the internal degrees of freedom. The systems are shown to be integrable and the spectrum and wavefunctions of the quantum version are derived.