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.
|Pages (from-to)||7 - 12|
|Number of pages||6|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|Publication status||Published - 20 Mar 2006|
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
Blasiak, P., Dattoli, G., Horzela, A., & Penson, K. A. (2006). Representations of monomiality principle with Sheffer-type polynomials and boson normal ordering. Physics Letters, Section A: General, Atomic and Solid State Physics, 352(1-2), 7 - 12. https://doi.org/10.1016/j.physleta.2005.11.052