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An Introduction to Tensors and Group Theory for Physicists

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The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional "invitation" sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students.

Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Examples and exercises are provided in each chapter for good practice in applying the presented material and techniques.

Prerequisites for this text include the standard lower-division mathematics and physics courses, though extensive references are provided for the motivated student who has not yet had these. Advanced undergraduate and beginning graduate students in physics and applied mathematics will find this textbook to be a clear, concise, and engaging introduction to tensors and groups.

**Reviews of the First Edition**

"[P]hysicist 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...[W]ith 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. [This] is a masterpiece of exposition and explanation that would win credit for even a seasoned author."

-Physics Today

"Jeevanjee's [text]* *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. 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."

-MAA Reviews

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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)"

Nadir Jeevanjee is a graduate student research assistant at the Lawrence Berkeley National Laboratory in Berkeley, CA.

Part I Linear Algebra and Tensors.- A Quick Introduction to Tensors.- Vector Spaces.- Tensors.- Part II Group Theory.- Groups, Lie Groups, and Lie Algebras.- Basic Representation Theory.- The Winger-Echart Theorem and Other Applications.- Appendix Complexifications of Real Lie Algebras and the Tensor Product Decomposition of sl(2,C)R.- References.- Index.

GOR010807293

An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee

Nadir Jeevanjee

Used - Good

Hardback

Birkhauser Verlag AG

2015-03-12

305

3319147935

9783319147932

N/A

Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

The book has been read but remains in clean condition. All pages are intact and the cover is intact. Some minor wear to the spine.