Representations of monomiality principle with Sheffer-type polynomials and boson normal ordering

We construct explicit representations of the Heisenberg-Weyl algebra [P, M] = I in terms of ladder operators acting in the space of Sheffertype 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. (c) 2005 Elsevier B.V. All rights reserved.