The Ruijsenaars-Schneider model

We seek to clarify some of the physical aspects of the Ruijsenaars-Schneider models. This important class of models was presented as a relativistic generalisation of the Calogero-Moser models (i.e. integrable particle dynamics with long range interactions on a line) but, as we shall argue, this description is misleading. It is far better to simply view the models as a one-parameter generalisation of Calogero-Moser models. By viewing the models as describing certain eigenvalue motions we can appreciate the generic nature of the models.