Self-Dual Yang-Mills and the Hamiltonian Structures of Integrable Systems

1992/11/16 by Jeremy Schiff, Schiff, Jeremy
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.hep-th/9211070

openalex publication_date 1992/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In recent years it has been shown that many, and possibly all, integrable systems can be obtained by dimensional reduction of self-dual Yang-Mills. I show how the integrable systems obtained this way naturally inherit bihamiltonian structure. I also present a simple, gauge-invariant formulation of the self-dual Yang-Mills hierarchy proposed by several authors, and I discuss the notion of gauge equivalence of integrable systems that arises from the gauge invariance of the self-duality equations (and their hierarchy); this notion of gauge equivalence may well be large enough to unify the many diverse existing notions.

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