An Introduction to Tensors and Group Theory for Physicists 2nd Edition by Nadir Jeevanjee (PDF)

Description

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

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐As an undergraduate in physics and pure math, I was often frustrated by the lack of mathematical precision in my physics classes, while simultaneously being frustrated by not being able to clarify those concepts with my pure math education in the math department, which was often significantly more abstract and unrelated physical applications.Over the years I’ve pored through many physics and math books trying to piece things together, and I’ve written notes on everything. This book is almost like someone took all of my notes, added more to them, made them more clear, and wrote a book.Jeevanjee has done a great service to generations of budding physicists who also have an interest in math and are dissatisfied with the fast and loose treatments of this stuff that abound in physics courses.I am teaching a mathematical methods course next Fall, and I plan to recommend this text to all of my students who are interested in learning about the concepts it contains in more depth, many of which I will only have time to cover superficially.

⭐This book was finally able to help me make some connections between mathematics and physics that had previously eluded me for years, including during my graduate physics studies. The fact that tensors can be thought of as “slotted machines” that output a real number when all the slots are filled with vectors is an incredibly helpful, and simple, analogy. This approach also does away with the traditional explanations of tensors as being “things that transform according to blah blah blah blah” that seems so circular. Jeevanjee’s discussion of tensors as operators is enlightening too. I highly recommend this book.

⭐A pretty good book for those who have had no previous experience with these subjects. But it is not a light read, especially for the totally uninitiated. My only complaint was that the binding of the spine came unglued after using the book just a few times-which was easily reglued with the right compound-but still……….

⭐Actually shows you what other books merely gloss over or hand-wave at, in full detail. Plenty of exercises and solved examples too.

⭐I just started it but it seems really good.

⭐If you’re looking to get into theoretical physics for real (and if you already have a solid background in multivariable calculus and linear algebra), then START WITH THIS BOOK. I can’t praise it highly enough.Once you’re proficient in advanced calculus and abstract LA (vector spaces and transformations), your next steps in theoretical physics are to learn tensors and group theory/representation theory. The latter will let you move forward in studying General Relativity, the former will let you move forward with the math behind the standard model, particle physics, etc. as well as comprehend relativity topics (both Special and General) on a deeper level.And since this book teaches both topics – tensors and group/representation theory pretty much from the ground up – this is the doorway that leads to all those riches! And unlike most other books I’ve come across (though to be fair there is PLENTY of great pedagogical material in theoretical physics), Jeevanjee’s door isn’t left just slightly ajar. It’s wide open. Which is to say: it’s fun but challenging, fairly rigorous (for physics) but fascinating, formal but conversational.In short: this is as close as theoretical physics ever gets to “breezy”, but somehow without sacrificing the main objective, which is to drive home a deep understanding. It’s a great balance of conceptual understanding (through well-formulated definitions, discussions, and examples) and calculational proficiency (through well-chosen exercises).If you’ve delved into these topics before and found yourself staring dumbly at a definition of a tensor or a Lie algebra, wondering “Okay, so but what IS it actually? And why do I care? And how will it help me to better understand THE UNIVERSE AT THE DEEPEST AND HIGHEST LEVELS WHICH IS WHY I STARTED DOWN THIS ROAD IN THE FIRST PLACE????” – well, then, this book is just for you.P.S. When you’re “done” with this one (you’ll find yourself going back to it again and again and again), I highly recommend moving on to a couple of other Springer titles: “Physics from Symmetry” and “Symmetry and the Standard Model.”

⭐Jeevanjee has clearly thought long and hard about the problems plaguing group-theory-in-physics related literature. Many of the books take Linear Algebra for granted, and pass tensors off as objects with some extra indices. Jeevanjee takes his time covering the necessary elements of these subjects in detail, so that the rest of the book sits on much more solid ground. He is not afraid of being formal, but only in the spirit of making things clearer. The book takes some time, as it is written in a fairly mathematical style. The reward of the formality is deeper understanding and the capacity to actually DO group theory on one’s own. It is a very well balanced book, which does a great job of being both logically meticulous and still entertaining and relevant to physics. My only criticism is that it does not cover the Poincare group and that it doesn’t touch on any applications to particle physics, which unfortunately left me again stuck with the older literature. But, if we are lucky, maybe Jeevanjee will get inspired and write a third edition.

⭐A very good account of the representation theory of classical Lie groups and algebras, as applied to physics.

⭐Fantastic book for physicists trying to learn about tensors and group theory, while not dumbing down the math. For me this is the book for learning about tensor operators in general and why the Wigner-Eckhart theorem is so important in theoretical physics. The author is also kind enough to provide many references to more advanced material if someone needs it, something I wish more introductory textbooks did.

⭐The rigourous proof of Wigner Eckart theorem alone makes this book worthed.

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