Noncommutative geometry and a class of completely integrable models

Abstract

We introduce a Hodge operator in a framework of noncommutative geometry. The complete integrability of 2-dimensional classical harmonic maps into groups (sigma-models or principal chiral models) is then extended to a class of 'noncommutative' harmonic maps into matrix algebras.

7 pages, Proc. 7th Colloquium on Quantum Groups and Integrable Systems

References in corpus (1)

• A Proposal for a Differential Calculus in Quantum Mechanics

Cited by in corpus (5)

• Bi-differential calculi and integrable models
• Bicomplexes and Integrable Models
• Bi-differential calculus and the KdV equation
• Pseudo-Riemannian Metrics in Models Based on Noncommutative Geometry
• Noncommutative Nonlinear Sigma Models and Integrability