Commutation Relations, Normal Ordering, and Stirling Numbers

Sprednja platnica
CRC Press, 18. sep. 2015 - 504 strani

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.

 

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Vsebina

Chapter 1 Introduction
1
Chapter 2 Basic Tools
23
Chapter 3 Stirling and Bell Numbers
51
Chapter 4 Generalizations of Stirling Numbers
79
Chapter 5 Generalizations of Stirling Numbers Normal Ordering
139
Chapter 6 Normal Ordering in the Weyl AlgebraFurther Aspects
183
Chapter 7 The qDeformed Weyl Algebra and the Meromorphic Weyl Algebra
225
Chapter 8 A Generalization of the Weyl Algebra
277
Appendix A Basic Definitions of qCalculus
399
Appendix B Symmetric Functions
401
Appendix C Basic Concepts in Graph Theory
403
Appendix D Definition and Basic Facts of Lie Algebras
405
Appendix E The BakerCampbellHausdorff Formula
409
Appendix F Hilbert Spaces and Linear Operators
411
Bibliography
419
Back Cover
481

Chapter 9 The qDeformed Generalized Weyl Algebra
341
Chapter 10 A Generalization of Touchard Polynomials
375

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O avtorju (2015)

Toufik Mansour is a professor at the University of Haifa. His research interests include enumerative combinatorics and discrete mathematics and its applications. He has authored or co-authored numerous papers in these areas, many of them concerning the enumeration of normal ordering. He earned a PhD in mathematics from the University of Haifa.

Matthias Schork is a member of the IT department at Deutsche Bahn, the largest German railway company. His research interests include mathematical physics as well as discrete mathematics and its applications to physics. He has authored or coauthored many papers focusing on Stirling numbers and normal ordering and its ramifications. He earned a PhD in mathematics from the Johann Wolfgang Goethe University of Frankfurt.

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