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Mathematical Physics

Title: 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.
Comments: 16 pages, LaTeX, uses amssymb
Subjects: Mathematical Physics (math-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA); Exactly Solvable and Integrable Systems (nlin.SI)
Report number: GOET-TP 99/97
Cite as: arXiv:physics/9712004 [math-ph]
  (or arXiv:physics/9712004v1 [math-ph] for this version)

Submission history

From: Folkert Muller-Hoissen [view email]
[v1] Mon, 1 Dec 1997 16:06:08 GMT (17kb)