Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice
Quantum Physics
2008-11-26 v1 High Energy Physics - Lattice
High Energy Physics - Theory
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.
Cite
@article{arxiv.quant-ph/9509014,
title = {Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice},
author = {A. Dimakis and F. Mueller-Hoissen and T. Striker},
journal= {arXiv preprint arXiv:quant-ph/9509014},
year = {2008}
}
Comments
19 pages, Latex