Deformed Bosons: Combinatorics of Normal Ordering

2); (2)LPTL; 3) ((1)Polish Academy of Sciences; (3)Open University; A. Horzela (1); A. I. Solomon (2; France; K. A. Penson (2); Krakow; Milton Keynes MK7 6AA

arxiv: quant-ph/0410226 · v1 · submitted 2004-10-27 · 🪐 quant-ph · math.CO

Deformed Bosons: Combinatorics of Normal Ordering

P. Blasiak (1 , 2) , A. Horzela (1) , K. A. Penson (2) , A. I. Solomon (2 , 3) ((1)Polish Academy of Sciences , Krakow , Poland

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(2)LPTL Paris University 6 France (3)Open University Milton Keynes MK7 6AA UK)

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keywords deformednormalorderingrespannihilationbosonicbosonscanonical

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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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Deformed Bosons: Combinatorics of Normal Ordering

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