Some aspects of noncommutative geometry and physics

Abstract

An introduction is given to some selected aspects of noncommutative geometry. Simple examples in this context are provided by finite sets and lattices. As an application, it is explained how the nonlinear Toda lattice and a discrete time version of it can be understood as generalized sigma-models based on noncommutative geometries. In particular, in this way one achieves a simple understanding of the complete integrability of the Toda lattice. Furthermore, generalized metric structures on finite sets and lattices are briefly discussed.

16 pages, LaTeX, uses amssymb

References in corpus (1)

• Connes' distance function on one-dimensional lattices

Cited by in corpus (7)

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• Wilson Action of Lattice Gauge Fields with An Additional Term from Noncommutative Geometry
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• Dirac-Connes Operator on Discrete Abelian Groups and Lattices
• On a correspondence principle between discrete differential forms, graph structure and multi-vector calculus on symmetric lattices
• A brief introduction to the noncommutative geometry description of particle physics standard model
• Deformations of classical geometries and integrable systems