Self-dual Hamiltonians as Deformations of Free Systems

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.

5 pages, LaTeX (corrected misprints)

References in corpus (4)

• Duality in Integrable Systems and Gauge Theories
• On Double-Elliptic Integrable Systems. 1. A Duality Argument for the case of SU(2)
• Commuting Hamiltonians from Seiberg-Witten Theta-Functions
• Seiberg-Witten theory and duality in integrable systems

Cited by in corpus (5)

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• On the status of DELL systems
• Characteristic determinant and Manakov triple for the double elliptic integrable system