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

P. Blasiak, G. Dattoli, A. Horzela, K.A. Penson

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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. © 2005 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)7 - 12
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number1-2
Publication statusPublished - 20 Mar 2006
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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