On Integrable Models Related to the $osp(1,2)$ Gaudin Algebra

TL;DR

This paper introduces the $osp(1,2)$ Gaudin algebra and explores integrable models like the Gaudin magnet and Dicke model, analyzing their properties and the impact of fermions on variable separation.

Contribution

It defines the $osp(1,2)$ Gaudin algebra and investigates related integrable models, including detailed analysis of simple cases and fermionic effects.

Findings

Analysis of the simplest models provided insights into their structure.

Fermions influence the separation of variables in these models.

The paper establishes a foundation for further study of $osp(1,2)$ related integrable systems.

Abstract

We define the $osp(1,2)$ Gaudin algebra and consider integrable models described by it. The models include the $osp(1,2)$ Gaudin magnet and the Dicke model related to it. Detailed discussion of the simplest cases of these models is presented. The effect of the presence of fermions on the separation of variables is indicated.