Deformed bosons: combinatorics of normal ordering

Blasiak, P.; Horzela, A.; Penson, K. A. and Solomon, A. I. (2004). Deformed bosons: combinatorics of normal ordering. Czechoslovak Journal of Physics, 54(11) pp. 1179–1184.

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

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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