Physics – Mathematical Physics
Scientific paper
2000-01-02
J. Phys. A: Math. Gen. 25 (1992) 2683-2691
Physics
Mathematical Physics
14 pages, Latex file
Scientific paper
10.1088/0305-4470/25/9/036
The normal ordering formulae for powers of the boson number operator $\hat{n}$ are extended to deformed bosons. It is found that for the `M-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = 1$, the extension involves a set of deformed Stirling numbers which replace the Stirling numbers occurring in the conventional case. On the other hand, the deformed Stirling numbers which have to be introduced in the case of the `P-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = q^{-\hat{n}}$, are found to depend on the operator $\hat{n}$. This distinction between the two types of deformed bosons is in harmony with earlier observations made in the context of a study of the extended Campbell-Baker-Hausdorff formula.
Katriel Jacob
Kibler Maurice
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