A Dimakis et al 1996 J. Phys. A: Math. Gen. 29 6861 doi:10.1088/0305-4470/29/21/017
A Dimakis
, F Müller-Hoissen
and T Striker![]()
`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.
Issue 21 (7 November 1996)
Received 24 June 1996
A Dimakis et al 1996 J. Phys. A: Math. Gen. 29 6861
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