Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice

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dc.creatorDimakis, A.
dc.creatorMueller-Hoissen, F.
dc.creatorStriker, T.
dc.date1995-09-21
dc.date.accessioned2026-07-07T10:59:05Z
dc.date.available2026-07-07T10:59:05Z
dc.description`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a lattice. Related ideas appeared in recent publications and we show that the examples treated there are special cases of umbral calculus. This observation then suggests various generalizations of these examples. A special umbral representation of the canonical commutation relations given in terms of the position and momentum operator on a lattice is investigated in detail.
dc.description19 pages, Latex
dc.identifierhttps://arxiv.org/abs/quant-ph/9509014
dc.identifierhttp://arxiv.org/abs/quant-ph/9509014
dc.identifierJ.Phys.A29:6861-6876,1996
dc.identifierdoi:10.1088/0305-4470/29/21/017
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/187328
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Lattice
dc.subjectHigh Energy Physics - Theory
dc.titleUmbral Calculus, Discretization, and Quantum Mechanics on a Lattice
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