Bi-differential calculi and integrable models
Mathematical Physics
2009-10-31 v2 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
solv-int
Abstract
The existence of an infinite set of conserved currents in completely integrable classical models, including chiral and Toda models as well as the KP and self-dual Yang-Mills equations, is traced back to a simple construction of an infinite chain of closed (respectively, covariantly constant) 1-forms in a (gauged) bi-differential calculus. The latter consists of a differential algebra on which two differential maps act. In a gauged bi-differential calculus these maps are extended to flat covariant derivatives.
Cite
@article{arxiv.math-ph/9908015,
title = {Bi-differential calculi and integrable models},
author = {Aristophanes Dimakis and Folkert Muller-Hoissen},
journal= {arXiv preprint arXiv:math-ph/9908015},
year = {2009}
}
Comments
24 pages, 2 figures, uses amssymb.sty and diagrams.sty, substantial extensions of examples (relative to first version)