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Deformed Bosons: Combinatorics of Normal Ordering

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Czechoslovak Journal of Physics Aims and scope

Abstract

We solve the normal ordering problem for (A † A)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.

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Authors and Affiliations

  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

    P. Blasiak

  2. H. Niewodniczański Institute of Nuclear Physics, Polish Acad. Sci., ul. Eliasza-Radzikowskiego 152, PL 31342 Krakow, Poland andrzej.horzela@ifj.edu.pl

    A. Horzela

  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

    K.A. Penson

  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

    A.I. Solomon

Authors
  1. P. Blasiak
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  2. A. Horzela
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  3. K.A. Penson
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  4. A.I. Solomon
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Blasiak, P., Horzela, A., Penson, K. et al. Deformed Bosons: Combinatorics of Normal Ordering. Czech J Phys 54, 1179–1184 (2004). https://doi.org/10.1007/s10582-004-9776-0

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  • DOI: https://doi.org/10.1007/s10582-004-9776-0

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