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Deformed Bosons: Combinatorics of Normal Ordering

P. Blasiak·A. Horzela·K. A. Penson·A. I. Solomon
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Abstract

We solve the normal ordering problem for (A* A)^n where A* (resp. A) are one mode deformed bosonic creation (resp. annihilation) operators satisfying [A,A*]=[N+1]-[N]. The solution generalizes results known for canonical and q-bosons. It involves combinatorial polynomials in the number operator N for which the generating functions and explicit expressions are found. Simple deformations provide examples of the method.

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P. Blasiak, A. Horzela, K. A. Penson, A. I. Solomon. 2004-10-27. Deformed Bosons: Combinatorics of Normal Ordering. https://doi.org/10.1007/s10582-004-9776-0

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