Monomiality principle, Sheffer-type polynomials and the normal ordering problem

We solve the boson normal ordering problem for (q(a†)a + v(a†))n with arbitrary functions q(x) and v(x) and integer n, where a and a† are boson annihilation and creation operators, satisfying [a, a†] 1. This consequently provides the solution for the exponential eλ(q(a†)a + v(a†)) generalizing the s...

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Bibliographic Details
Published in:Journal of physics. Conference series 2006-02, Vol.30 (1), p.86-97
Main Authors: Penson, K A, Blasiak, P, Dattoli, G, Duchamp, G H E, Horzela, A, Solomon, A I
Format: Article
Language:English
Subjects:
Combinatorial analysis
Mathematical analysis
Physics
Polynomials
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Summary:We solve the boson normal ordering problem for (q(a†)a + v(a†))n with arbitrary functions q(x) and v(x) and integer n, where a and a† are boson annihilation and creation operators, satisfying [a, a†] 1. This consequently provides the solution for the exponential eλ(q(a†)a + v(a†)) generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/30/1/012