Distances on a Lattice from Non-commutative Geometry

Details Distances on a Lattice from Non-commutative Geometry Distances on a Lattice from Non-commutative Geometry

1994-04-13

arxiv.org/abs/hep-lat/9404007v2

Phys.Lett. B341 (1994) 139-146

Physics

High Energy Physics

High Energy Physics - Lattice

14 pages

Scientific paper

10.1016/0370-2693(94)90302-6

Using the tools of noncommutative geometry we calculate the distances between the points of a lattice on which the usual discretized Dirac operator has been defined. We find that these distances do not have the expected behaviour, revealing that from the metric point of view the lattice does not look at all as a set of points sitting on the continuum manifold. We thus have an additional criterion for the choice of the discretization of the Dirac operator.

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