Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice

  title={Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice},
  author={Aristophanes Dimakis and Folkert Mueller-Hoissen and T. Striker},
  journal={Journal of Physics A},
`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… Expand
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