An Introduction to Tensors and Group Theory for Physicists

Authors: Jeevanjee, Nadir

  • Ideal for self-study or for use in the classroom
  • Includes many physical applications, particularly in quantum physics and relativity
  • Provides ample exercises for practice of the definitions and techniques
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  • ISBN 978-0-8176-4715-5
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About this Textbook

An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory.

Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to classical and quantum physics through the use of tensor products. Part II introduces abstract groups along with matrix Lie groups and Lie algebras, then intertwines this material with that of Part I by introducing representation theory.  Exercises and examples are provided throughout for good practice in applying the presented definitions and techniques. Advanced undergraduate and graduate students in physics and applied mathematics will find clarity and insight into the subject in this textbook.

Reviews

From the reviews:

“With An Introduction to Tensors and Group Theory for Physicists, physicist Nadir Jeevanjee has produced a masterly book that will help other physicists understand those subjects [tensors and groups] as mathematicians understand them… From the first pages, Jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern mathematical view. In contrast to the usual description of a baffling beast bristling with indices, Jeevanjee describes how, as he puts it, tensors eat vectors and spit out numbers. He combines vivid use of language with coherent expositions of the detailed equations and expressions. Above all, with compelling force and clarity, he provides many carefully worked-out examples and well-chosen specific problems… Jeevanjee’s clear and forceful writing presents familiar cases with a freshness that will draw in and reassure even a fearful student. He does not stint the technical details, which are nicely embedded in the text so that they connect smoothly with the larger conceptual exposition… An Introduction to Tensors and Group Theory for Physicists, written during Jeevanjee’s graduate studies at the University of California, Berkeley, is a masterpiece of exposition and explanation that would win credit for even a seasoned author. One can only hope that, after this prodigious first book, he will write many more.”

—Physics Today

"Jeevanjee’s An Introduction to Tensors and Group Theory for Physicists is a valuable piece of work on several counts, including its express pedagogical service rendered to fledgling physicists and the fact that it does indeed give pure mathematicians a way to come to terms with what physicists are saying with the same words we use, but with an ostensibly different meaning: it’s the same meat and potatoes, really, but the flavoring is all different.

Oh yes, one more thing. The book is very easy to read, very user-friendly, full of examples...and exercises, and will do the job the author wants it to do with style. I am indeed going to use it myself, hopefully to great advantage, in my upcoming dealings with my working-group."

—MAA Reviews

“The book is divided into two distinct parts, the first one (Chapters 1-3) dealing with linear algebra and tensors, the second focusing on group theory in physics (Chapter 4-6). … provide a solid background for students, helping them to understand the more advanced literature on the subject without formal difficulties. … this book not only fills a considerable pedagogical gap in the physical and mathematical literature, but also shows to what extent the material arises naturally within any consistent model of natural phenomena.” (Rutwig Campoamor-Stursberg, Mathematical Reviews, Issue 2012 i)

“The aim of the monograph is to fill a definite gap in literature by connecting the component formalism intrinsic to physical computations to the abstract but more conceptual formulations of mathematical literature and to present interconnections between tensor analysis and group theory, to demonstrate their physical applications. … It is destined for students of advanced-undergraduate level. … Every chapter in endowed by exercises and problems.” (Boris V. Loginov, Zentralblatt MATH, Vol. 1229, 2012)


Table of contents (6 chapters)

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-0-8176-4715-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Tensors and Group Theory for Physicists
Authors
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LCC
eBook ISBN
978-0-8176-4715-5
DOI
10.1007/978-0-8176-4715-5
Edition Number
1
Number of Pages
XVI, 242
Number of Illustrations and Tables
12 b/w illustrations
Topics