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 …

Combinatorics and Number Theory of Counting Sequences is an introduction to the theory
of finite set partitions and to the enumeration of cycle decompositions of permutations. The …

We discuss a general combinatorial framework for operator ordering problems by applying it
to the normal ordering of the powers and exponential of the boson number operator. The …

A new family of generalized Stirling and Bell numbers is introduced by considering powers
$(VU)^ n $ of the noncommuting variables $ U, V $ satisfying $ UV= VU+ hV^ s $. The case …

Abstract The generalized Stirling numbers Ss; h (n, k) introduced recently by the authors are
shown to be a special case of the three parameter family of generalized Stirling numbers S …

We provide the solution to the normal ordering problem for powers and exponentials of two
classes of operators. The first one consists of boson strings and more generally …

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 …

The Stirling numbers of the second kind nk (counting the number of partitions of a set of size
n into k non-empty classes) satisfy the relation (x D) nf (x)=∑ k≥ 0 nkxk D kf (x) where f is an …

Combinatorial aspects of normal ordering for annihilation and creation operators of a multi-
mode boson system are discussed. The modes are assumed to be coupled, since otherwise …