Abstract
In this Letter, we continue the work of Bimonte, Lizzi and Sparano on distances on a one-dimensional lattice. We succeed in analytically proving the exact formulae for such distances. We find that the distance to an even point on the lattice is the geometrical average of the ‘predecessor’ and ‘successor’ distances to the neighbouring odd points.
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Refernces
Bimonte, G., Lizzi, F. and Sparano, G.: Distances on a lattice from noncommutative geometry, Phys. Lett. B 341 (1994), 139–146.
Connes, A.: Noncommutative Geometry, Academic Press, New York, 1994.
Gantmacher, F. R.: Applications of the Theory of Matrices, Interscience, New York, 1959.
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Atzmon, E. Distances on a one-dimensional lattice from noncommutative geometry. Letters in Mathematical Physics 37, 341–348 (1996). https://doi.org/10.1007/BF00343197
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DOI: https://doi.org/10.1007/BF00343197