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Monomiality principle, Sheffer-type polynomials and the normal ordering problem

Penson, K.A.; Blasiak, P.; Dattoli, G.; Duchamp, G.H.E.; Horzela, A. and Solomon, A.I. (2006). Monomiality principle, Sheffer-type polynomials and the normal ordering problem. Journal of Physics: Conference Series, 30 pp. 86–97.

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DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1088/1742-6596/30/1/012
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Abstract

We solve the boson normal ordering problem for
(q(a�)a + v(a�))^n with arbitrary functions q(x) and v(x) and integer n, where a and a' are boson annihilation and creation operators, satisfying [a, a�] = 1. This consequently provides the solution for the exponential
exp(?(q(a�)a + v(a�))) generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.

Item Type: Journal Article
ISSN: 1742-6588
Keywords: boson ordering;Sheffer; monomiality; shift operator
Academic Unit/Department: Science > Physical Sciences
Item ID: 6303
Depositing User: Allan Solomon
Date Deposited: 24 Jan 2007
Last Modified: 26 Jan 2011 10:46
URI: http://oro.open.ac.uk/id/eprint/6303
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