Combinatorial solutions to normal ordering of bosons |
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| Authors: | P Blasiak A Gawron A Horzela K A Penson A I Solomon |
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| Institution: | (1) H. Niewodniczanski Institute of Nuclear Physics, Polish Acad. Sci., ul. Eliasza-Radzikowskiego 152, PL 31342 Krakow, Poland;(2) Laboratoire de Physique Theorique de la Matiere Condensee, Universite P. et M. Curie, Tour 24 - 2e et., 4 Pl. Jussieu, F 75252 Paris Cedex 05, France;(3) Present address: Laboratoire de Physique Theorique de la Matiere Condensee, Universite P. et M. Curie, Tour 24 - 2e et., 4 Pl. Jussieu, F 75252 Paris Cedex 05, France;(4) Physics and Astronomy Department, The Open University, Milton Keynes, MK7 6AA, U.K. |
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| Abstract: | We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of
standard combinatorial notions — the Stirling and Bell numbers, Bell polynomials and Dobinski relations — lead to calculational
tools, which allow to find explicitly normally ordered forms for a large class of operator functions.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005. |
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| Keywords: | boson normal ordering coherent states combinatorics |
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