Integrable Models From Twisted Half Loop Algebras

TL;DR

This paper constructs new integrable quantum models using subalgebras of half loop algebras, demonstrating their integrability and symmetries in twisted Gaudin magnets and Calogero-type particle systems.

Contribution

It introduces novel integrable models based on twisted half loop algebra subalgebras, expanding the algebraic framework for quantum integrable systems.

Findings

Proves algebraic properties of subalgebras using St Petersburg school notation

Demonstrates integrability of twisted Gaudin magnets

Establishes symmetries of Calogero-type models

Abstract

This paper is devoted to the construction of new integrable quantum mechanical models based on certain subalgebras of the half loop algebra of gl(N). Various results about these subalgebras are proven by presenting them in the notation of the St Petersburg school. These results are then used to demonstrate the integrability, and find the symmetries, of two types of physical system: twisted Gaudin magnets, and Calogero-type models of particles on several half-lines meeting at a point.