A time-discretized version of the Calogero-Moser model

TL;DR

This paper presents a new integrable time-discretized Calogero-Moser model derived from pole solutions of a discretized KP equation, maintaining key structures like the Lax pair and invariants, and converging to the original model in the continuum limit.

Contribution

It introduces a novel discrete version of the Calogero-Moser model with preserved integrability features and a consistent continuum limit.

Findings

Constructed a finite-dimensional symplectic mapping for the discrete model

Derived the Lax pair and invariants for the discretized system

Showed the classical r-matrix matches the continuum model

Abstract

We introduce an integrable time-discretized version of the classical Calogero-Moser model, which goes to the original model in a continuum limit. This discrete model is obtained from pole solutions of a discretized version of the Kadomtsev-Petviashvili equation, leading to a finite-dimensional symplectic mapping. Lax pair, symplectic structure and sufficient set of invariants of the discrete Calogero-Moser model are constructed. The classical $r$-matrix is the same as for the continuum model.