Sklyanin Bracket and Deformation of the Calogero-Moser System

TL;DR

This paper constructs a deformed integrable system related to the Calogero-Moser model using symplectic reduction with Sklyanin algebra, explicitly solves its classical equations, and performs quantization.

Contribution

It introduces a new deformation of the Calogero-Moser system via Sklyanin algebra and provides explicit solutions and quantization methods.

Findings

Explicit classical equations of motion solved

Deformation of Calogero-Moser system constructed

Quantization of the deformed system achieved

Abstract

A two-dimensional integrable system being a deformation of the rational Calogero-Moser system is constructed via the symplectic reduction, performed with respect to the Sklyanin algebra action. We explicitly resolve the respective classical equations of motion via the projection method and quantize the system.