Commutation Relations, Normal Ordering, and Stirling Numbers Page 1 Commutation
Relations, Normal Ordering, and Stirling Numbers Toufik Mansour • Matthias Schork Mansour • …

Quantum physics has revealed many interesting formal properties associated with the
algebra of two operators, A and B, satisfying the partial commutation relation AB-BA= 1. This …

In this communication, we consider the normal ordering of operators of the type where a
(resp. a+) is a boson annihilation (resp. creation) operator; these satisfy [a, a+]≡ aa+− a+ a …

Umbral extensions of the stirling numbers of the second kind are considered and the
resulting dobinski-like various formulas including new ones are presented. These …

We consider the transformation properties of integer sequences arising from the normal
ordering of exponentiated boson ([a, a†]= 1) monomials of the form exp [λ (a†) ra], r= 1, 2 …

We consider properties of the operators D (r, M)= ar (a† a) M (which we call generalized
Laguerre-type derivatives), with r= 1, 2,…⁠, M= 0, 1,…⁠, where a and a† are boson …

The general normal ordering problem for boson strings is a combinatorial problem. In this
talk we restrict ourselves to single-mode boson monomials. This problem leads to elegant …

We construct and analyze a family of coherent states built on sequences of integers
originating from the solution of the boson normal ordering problem. These sequences …

Constructions of space-time codes having amplitude-modulated phase-shift keying (AM-
PSK) constellations are presented in this paper. The first construction, termed p-radii …

We introduce a generalization of the Dobiński relation through which we define a family of
Bell-type numbers and polynomials. For all these sequences, we find the weight function of …