Commutation Relations, Normal Ordering, and Stirling Numbers
Autor Toufik Mansour, Matthias Schorken Limba Engleză Hardback – 21 sep 2015
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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Specificații
ISBN-13: 9781466579880
ISBN-10: 1466579889
Pagini: 528
Ilustrații: 20 black & white illustrations, 5 black & white tables
Dimensiuni: 178 x 254 x 33 mm
Greutate: 1.48 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
ISBN-10: 1466579889
Pagini: 528
Ilustrații: 20 black & white illustrations, 5 black & white tables
Dimensiuni: 178 x 254 x 33 mm
Greutate: 1.48 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Cuprins
Introduction. Basic Tools. Stirling and Bell Numbers. Generalizations of Stirling Numbers. The Weyl Algebra, Quantum Theory, and Normal Ordering. Normal Ordering in the Weyl Algebra—Further Aspects. The q-Deformed Weyl Algebra and the Meromorphic Weyl Algebra. A Generalization of the Weyl Algebra. The q-Deformed Generalized Weyl Algebra. A Generalization of Touchard Polynomials. Appendices.
Notă biografică
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.
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.
Descriere
This book provides an introduction to the combinatorial aspects of normal ordering in the Weyl algebra and some of its close relatives. It discusses the Stirling numbers, closely related generalizations, and their role as normal ordering coefficients in the Weyl algebra. In addition to the combinatorial aspects, the book presents the relation to operational calculus and describes the physical motivation for ordering words in the Weyl algebra arising from quantum theory, along with some applications.