Self-dual Hamiltonians as Deformations of Free Systems

TL;DR

This paper explores self-dual Hamiltonians as deformations of free systems on symplectic manifolds, highlighting examples like double elliptic Hamiltonians and their relation to integrable systems.

Contribution

It introduces a framework for understanding self-dual Hamiltonians as deformations of free systems and discusses explicit examples including recent double elliptic Hamiltonians.

Findings

Self-dual Hamiltonians can be viewed as deformations of free systems.

Explicit examples include double elliptic Hamiltonians.

Duality in integrable systems is a derivative notion from self-duality.

Abstract

We formulate the problem of finding self-dual Hamiltonians (associated with integrable systems) as deformations of free systems given on various symplectic manifolds and discuss several known explicit examples, including recently found double elliptic Hamiltonians. We consider as basic the notion of self-duality, while the duality in integrable systems (of the Toda/Calogero/Ruijsenaars type) comes as a derivative notion (degenerations of self-dual systems). This is a talk presented at the Workshop "Classical and Quantum Integrable Systems", Protvino, January, 2001.