Pythagoras' Theorem on a 2D-Lattice from a "Natural" Dirac Operator and Connes' Distance Formula

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dc.creatorDai, Jian
dc.creatorSong, Xing-Chang
dc.date2001-01-15
dc.date.accessioned2026-07-07T10:53:30Z
dc.date.available2026-07-07T10:53:30Z
dc.descriptionOne of the key ingredients of A. Connes' noncommutative geometry is a generalized Dirac operator which induces a metric(Connes' distance) on the state space. We generalize such a Dirac operator devised by A. Dimakis et al, whose Connes' distance recovers the linear distance on a 1D lattice, into 2D lattice. This Dirac operator being "naturally" defined has the so-called "local eigenvalue property" and induces Euclidean distance on this 2D lattice. This kind of Dirac operator can be generalized into any higher dimensional lattices.
dc.descriptionLatex 11pages, no figures
dc.identifierhttps://arxiv.org/abs/hep-th/0101092
dc.identifierhttp://arxiv.org/abs/hep-th/0101092
dc.identifierJ.Phys.A34:5571-5582,2001
dc.identifierdoi:10.1088/0305-4470/34/27/307
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185505
dc.subjectHigh Energy Physics - Theory
dc.subjectHigh Energy Physics - Lattice
dc.subjectMathematical Physics
dc.titlePythagoras' Theorem on a 2D-Lattice from a "Natural" Dirac Operator and Connes' Distance Formula
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