ABSTRACT

Commutation Relations, Normal Ordering, and Stirling Numbers provides an introduction to the combinatorial aspects of normal ordering in the Weyl algebra and some of its close relatives. The Weyl algebra is the algebra generated by two letters U and V subject to the commutation relation UV - VU = I. It is a classical result that normal ordering pow

chapter 1|22 pages

Introduction

chapter 2|28 pages

Basic Tools

chapter 3|28 pages

Stirling and Bell Numbers

chapter 4|60 pages

Generalizations of Stirling Numbers

chapter 8|64 pages

A Generalization of the Weyl Algebra

chapter 9|34 pages

The q-Deformed Generalized Weyl Algebra

chapter 10|24 pages

A Generalization of Touchard Polynomials