Combinatorical and Algebraic Structures Seminar

Date:	24.3.2006
Speaker:	Pavel Blasiak, Institute of Nuclear Physics, Krakow
Title:	Combinatorics of boson normal ordering
Abstract:	(spoluautoři: A. Horzela) We consider the problem of normal ordering of boson creation and annihilation operators and provide the solution for two large classes of operators. The first one consists of boson strings and more generally homogeneous polynomials, while the second one treats operators linear in one of the creation or annihilation operators. Both solutions generalize Bell and Stirling numbers arising in the number operator case. In the solution we use the advanced combinatorial analysis to provide closed form expressions, generating functions, recurrences, etc. The analysis is based on the Dobinski-type relations and the umbral calculus methods. We point out the combinatorial interpretation of such obtained structures and illustrate this framework by applications to the construction of generalized coherent states, operator calculus and ordering of deformed bosons.

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