Commutation Relations, Normal Ordering, and Stirling Numbers

Description

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 powers of VU involve the Stirling numbers. The book is a one-stop reference on the research activities and known results of normal ordering and Stirling numbers. It discusses the Stirling numbers, closely related generalizations, and their role as normal ordering coefficients in the Weyl algebra. The book also considers several relatives of this algebra, all of which are special cases of the algebra in which UV − qVU = hVs holds true. The authors describe combinatorial aspects of these algebras and the normal ordering process in them. In particular, they define associated generalized Stirling numbers as normal ordering coefficients in analogy to the classical Stirling numbers. In addition to the combinatorial aspects, the book presents the relation to operational calculus, describes the physical motivation for ordering words in the Weyl algebra arising from quantum theory, and covers some physical applications. Front Cover Contents List of Figures List of Tables Preface Acknowledgment About the Authors Chapter 1 Introduction Chapter 2 Basic Tools Chapter 3 Stirling and Bell Numbers Chapter 4 Generalizations of Stirling Numbers Chapter 5 Generalizations of Stirling Numbers Normal Ordering Chapter 6 Normal Ordering in the Weyl Algebra-Further Aspects Chapter 7 The q-Deformed Weyl Algebra and the Meromorphic Weyl Algebra Chapter 8 A Generalization of the Weyl Algebra Chapter 9 The q-Deformed Generalized Weyl Algebra Chapter 10 A Generalization of Touchard Polynomials Appendix A Basic Definitions of q-Calculus Appendix B Symmetric Functions Appendix C Basic Concepts in Graph Theory Appendix D Definition and Basic Facts of Lie Algebras Appendix E The Baker–Campbell–Hausdorff Formula Appendix F Hilbert Spaces and Linear Operators Bibliography Back Cover