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Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice | | A. Dimakis
; F. Mueller-Hoissen
; T. Striker
; | | Date: |
21 Sep 1995 | | Journal: | J.Phys. A29 (1996) 6861-6876 | | Subject: | quant-ph hep-lat hep-th | | Affiliation: | Iraklion), F. Mueller-Hoissen (Goettingen), T. Striker (Goettingen | | Abstract: | `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. | | Source: | arXiv, quant-ph/9509014 | | Services: | Forum | Review | PDF | Favorites | |
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