Some aspects of noncommutative geometry and physics

1997/12/01 by Aristophanes Dimakis, A. Dimakis, Dimakis, A. +3 · 6 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #gr-qc #hep-th #math-ph #math.MP #math.QA #nlin.SI

paper · pdf · doi:10.48550/arxiv.physics/9712004

16 pages, LaTeX, uses amssymb

arxiv created 1997/12/01 · arxiv updated 2009/11/30

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.

Cited by

• 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
• Dirac-Connes Operator on Discrete Abelian Groups and Lattices
• Wilson Action of Lattice Gauge Fields with An Additional Term from Noncommutative Geometry
• Deformations of classical geometries and integrable systems
• Dynamical evolution in non-commutative discrete phase space and the derivation of classical kinetic equations

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