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Deformed Bosons: Combinatorics of Normal Ordering

Authors:	P. Blasiak A. Horzela K.A. Penson A.I. Solomon

Affiliation:	(1) Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, Tour 24 - 2e ét., 4 Pl. Jussieu, F 75252 Paris Cedex 05, France blasiak@lptl.jussieu.fr;(2) H. Niewodniczaski Institute of Nuclear Physics, Polish Acad. Sci., ul. Eliasza-Radzikowskiego 152, PL 31342 Krakow, Poland andrzej.horzela@ifj.edu.pl;(3) Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, Tour 24 - 2e ét., 4 Pl.Jussieu, F 75252 Paris Cedex 05, France penson@lptl.jussieu.fr;(4) Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, Tour 24 - 2e ét., 4 Pl.Jussieu, F 75252 Paris Cedex 05, France a.i.solomon@open.ac.uk

Abstract:	We solve the normal ordering problem for (AA)ⁿ where A and A are one mode deformed ([A,A] = [N+1] – [N]) bosonic ladder operators. The solution generalizes results known for canonical bosons. It involves combinatorial polynomials in the number operator N for which the generating function and explicit expressions are found. Simple deformations provide examples of the method.

Keywords:	boson normal ordering combinatorics
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