Commutation Relations, Normal Ordering, and Stirling Numbers

Toufik Mansour (University of Haifa, Israel), Matthias Schork

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English

CRC Press Inc
21 September 2015

Discrete mathematics; Combinatorics & graph theory; Applied mathematics; Mathematical physics; Life sciences: general issues

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.

By: Toufik Mansour (University of Haifa Israel), Matthias Schork
Imprint: CRC Press Inc
Country of Publication: United States
Dimensions: Height: 254mm, Width: 178mm, Spine: 33mm
Weight: 1.133kg
ISBN: 9781466579880
ISBN 10: 1466579889
Pages: 504
Publication Date: 21 September 2015
Audience: College/higher education , General/trade , Primary , ELT Advanced
Format: Hardback
Publisher's Status: Active

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.