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

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

1992-11-16

arxiv.org/abs/hep-th/9211070v1

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, no figures, plain tex, IASSNS-HEP-92/34

Scientific paper

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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