A New Approach to Functional Analysis on Graphs, the Connes-Spectral Triple and its Distance Function

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dc.creatorRequardt, M.
dc.date1997-08-04
dc.date1997-10-14
dc.date.accessioned2026-07-07T09:08:22Z
dc.date.available2026-07-07T09:08:22Z
dc.descriptionContinuing previous work we develop a certain piece of functional analysis on general graphs and use it to create what Connes calls a 'spectral triple', i.e. a Hilbert space structure, a representation of a certain (function) algebra and a socalled 'Dirac operator', encoding part of the geometric/algebraic properties of the graph. We derive in particular an explicit expression for the 'Connes-distance function' and show that it is in general bounded from above by the ordinary distance on graphs (being, typically, strictly smaller(!) than the latter). We exhibit, among other things, the underlying reason for this phenomenon.
dc.description18 pages, Latex, section 3 about functional analysis expanded, some proofs more detailed
dc.identifierhttps://arxiv.org/abs/hep-th/9708010
dc.identifierhttp://arxiv.org/abs/hep-th/9708010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150697
dc.subjectHigh Energy Physics - Theory
dc.subjectFunctional Analysis
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectQuantum Algebra
dc.titleA New Approach to Functional Analysis on Graphs, the Connes-Spectral Triple and its Distance Function
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