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Commutation Relations, Normal Ordering, and Stirling Numbers (Discrete Mathematics and Its Applications), by Toufik Mansour, Matthias Scho
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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.
- Sales Rank: #1820851 in Books
- Published on: 2015-09-21
- Original language: English
- Number of items: 1
- Dimensions: 10.00" h x 1.30" w x 7.10" l, .0 pounds
- Binding: Hardcover
- 528 pages
About the Author
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.
Most helpful customer reviews
0 of 0 people found the following review helpful.
Deep and engaging
By D Zeilberger
This is a masterpiece blending very elegant combinatorics that is very important in physics and abstract algebra.
The mathematics is deep, the exposition very engaging, and the historical narrative very insightful.
Highly recommended to anyone who is interested in how combinatorics can be applied to produce both pure and applied knowledge.
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