Integrable Discretizations of Chiral Models

Abstract

A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprises corresponding discrete versions. This is achieved via a deformation of the ordinary differential calculus. In particular, the nonlinear Toda lattice results in this way from the linear (continuum) wave equation. The method is applied to several further examples. We also construct Lax pairs and Bäcklund transformations for the class of models considered in this work.

14 pages, Latex

References in corpus (1)

• Differential Calculi on Commutative Algebras

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• Differential Geometry of Group Lattices
• Some aspects of noncommutative geometry and physics
• The Generalized Moyal Nahm and Continuous Moyal Toda Equations
• Noncommutative geometry and a class of completely integrable models
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• Pseudo-Riemannian Metrics in Models Based on Noncommutative Geometry
• Deformations of classical geometries and integrable systems