Compactified Trigonometric Ruijsenaars-Schneider Systems

Tamás Görbe, University of Leeds

The compactified Ruijsenaars-Schneider (RS) models are obtained from the standard RS systems (aka relativistic Calogero-Sutherland systems) by Wick rotation. Models with trigonometric potentials describe particles moving on a circle with a chord distance-dependent pairwise interaction. Moreover the compactified Hamiltonians are periodic not only in the position variables x, but also in the momenta p. Surprisingly, there are two dramatically different types of dynamics (distinguished by the value of the coupling parameter). For type (i) couplings particle distances have lower (and upper) bounds, while type (ii) couplings allow particle collisions to happen resulting in a more complicated dynamics. We will present the global phase space and quantization of models with type (i) couplings.

Based on joint work with László Fehér and Martin Hallnäs.