Representations of Monomiality Principle with Sheffer-type Polynomials and Boson Normal Ordering

Abstract

We construct explicit representations of the Heisenberg-Weyl algebra [P,M]=1 in terms of ladder operators acting in the space of Sheffer-type polynomials. Thus we establish a link between the monomiality principle and the umbral calculus. We use certain operator identities which allow one to evaluate explicitly special boson matrix elements between the coherent states. This yields a general demonstration of boson normal ordering of operator functions linear in either creation or annihilation operators. We indicate possible applications of these methods in other fields.

9 pages

References in corpus (2)

• Boson Normal Ordering via Substitutions and Sheffer-type Polynomials
• Canonical Commutation Relation Preserving Maps

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