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An Introduction to Tensors and Group Theory for Physicists [Hardcover]

Nadir Jeevanjee
4.9 out of 5 stars  See all reviews (10 customer reviews)

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Book Description

August 25, 2011 0817647147 978-0817647148 2011

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. Advanced undergraduate and graduate students in physics and applied mathematics will find clarity and insight into the subject in this textbook.


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Editorial Reviews

Review

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)

From the Back Cover

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.


Product Details

  • Hardcover: 242 pages
  • Publisher: Birkhäuser; 2011 edition (August 25, 2011)
  • Language: English
  • ISBN-10: 0817647147
  • ISBN-13: 978-0817647148
  • Product Dimensions: 9.1 x 6.3 x 0.8 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.9 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #272,191 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
35 of 35 people found the following review helpful
By AcedOut
Format:Hardcover|Verified Purchase
I read this book during my first year of graduate school. For a little background, I was a math and physics double major as an undergraduate, but I didn't take any courses on Tensors or Lie Groups, which is why I decided to look into this text.

This book introduces Tensors and Group Theory with far more rigor than you normally get within a Physics classroom, grad or undergrad. If you don't have a mathematics background, you should be OK looking at this book. While it certainly helps to have exposure to proof based math, the book starts at the foundations of groups and linear algebra so all the topics build naturally. In short, you will never be lost if you read carefully, so it's also perfect for an advanced undergraduate as well.

The underlying mathematical structure of Physics that is covered in this text is usually only superficially learned through rote problem solving during grad school. This is a significant deficiency in graduate Physics pedagogy that this book concisely addresses. It's a shame no one has written something this accessible sooner.

The author is very good at breaking the concepts down in his exposition. It is definitely worth rereading from time to time, as there is usually a new insight to be gained from the text. The exercises and examples in the book are also well chosen. They are usually pretty short, but very illustrative. It's pretty much always clear how the concepts tie to Physics when you work through them.

In short, I found this book to be extremely helpful. It provides a good framework to understand much of the advanced mathematics that one encounters in graduate school.
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6 of 6 people found the following review helpful
5.0 out of 5 stars Pedagogical and Modern January 4, 2013
Format:Hardcover
This book gives a self-contained introduction to tensors and group theory in a very pedagogical style. It moves quickly and stays interesting without losing the reader. My favorite thing about it is the quasi-rigorous approach: rather than proving every statement, Jevanjee provides references to other authors for the proofs and instead focuses primarily on definitions, concepts, and examples. He also takes a thoroughly modern perspective (e.g. tensors are linear functions), though not without making helpful connections to the older terminology used frequently in physics books.
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2 of 2 people found the following review helpful
5.0 out of 5 stars Very clear language and mathematics August 7, 2013
Format:Hardcover|Verified Purchase
Jeevanjee's textbook is excellent. I am a Materials Scientist with a Physics background, and yet tensors have always been a little mysterious to me. This text lays the mathematical framework you need in order to understand tensors (and group theory), while providing concrete examples in physical contexts; everything is exceptionally clear and easy to understand. I highly recommend this book to any Physicist who feels the way I used to feel about tensors (i.e. you can work the math, but don't have a clear understanding of why it's working). Great text.
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1 of 1 people found the following review helpful
5.0 out of 5 stars Clear, lucid, and immensely helpful January 27, 2014
Format:Hardcover
This book is a valuable resource and a service to the community. The author not only seems to have a deep appreciation for mathematics, but also great insight into the mind of budding physicists. Many thumbs up!
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1 of 1 people found the following review helpful
5.0 out of 5 stars Useful and very understandable January 10, 2014
Format:Hardcover|Verified Purchase
Very understandable exposition of tensors theory for the needing of Mathematical Physics (that is, Rational Mechanics, Quantum Mechanics and General Relativity). Also useful the equally large part about Lie Groups and Algebra. It is not about calculations (for this you can take a Schaum) but about the nature of tensors: it gives you the sensation of finally grasping the meaning of these objects, beyond usual definitions. Nice english also for the foreigner. Recommended to students. Worth the price.
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