Calogero-Moser-Sutherland systems

Abstract

We discuss integrable many-body systems in one dimension of Calogero-Moser-Sutherland type, both classical and quantum as well as nonrelativistic and relativistic. In particular, we consider fundamental properties such as integrability, the existence of explicit solutions as well as action-angle and bispectral dualities that relate different such systems. We also briefly discuss the early history of the subject and indicate connections with other integrable systems.

20 pages. Invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. In v2 we have made some minor revisions and corrections