Deformed Bosons: Combinatorics of Normal Ordering
P. Blasiak, A. Horzela, K. A. Penson, A. I. Solomon
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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