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

By Nadir Jeevanjee

The moment version of this hugely praised textbook offers an advent to tensors, crew idea, and their purposes in classical and quantum physics. either intuitive and rigorous, it goals to demystify tensors by means of giving the marginally extra summary yet conceptually a lot clearer definition present in the mathematics literature, after which connects this formula to the part formalism of physics calculations. New pedagogical positive factors, corresponding to new illustrations, tables, and boxed sections, in addition to extra “invitation” sections that supply available introductions to new fabric, provide elevated visible engagement, readability, and motivation for students.

Part I starts with linear algebraic foundations, follows with the trendy component-free definition of tensors, and concludes with purposes to physics by using tensor items. half II introduces team thought, together with summary teams and Lie teams and their linked Lie algebras, then intertwines this fabric with that of half I by way of introducing illustration thought. Examples and workouts are supplied in every one bankruptcy for reliable perform in using the offered fabric and techniques.

Prerequisites for this article comprise the traditional lower-division arithmetic and physics classes, although large references are supplied for the encouraged scholar who has no longer but had those. complicated undergraduate and starting graduate scholars in physics and utilized arithmetic will locate this textbook to be a transparent, concise, and fascinating advent to tensors and groups.

Reviews of the 1st Edition

“[P]hysicist Nadir Jeevanjee has produced a masterly e-book that might support different physicists comprehend these matters [tensors and teams] as mathematicians comprehend them… From the 1st pages, Jeevanjee indicates remarkable ability find clean, compelling phrases to deliver ahead the perception that animates the trendy mathematical view…[W]ith compelling strength and readability, he offers many conscientiously worked-out examples and well-chosen particular difficulties… Jeevanjee’s transparent and forceful writing offers known situations with a freshness that might attract and reassure even a apprehensive scholar. [This] is a masterpiece of exposition and clarification that will win credits for even a professional author.”

—Physics Today

"Jeevanjee’s [text]is a invaluable piece of labor on a number of counts, together with its exhibit pedagogical provider rendered to fledgling physicists and the truth that it does certainly supply natural mathematicians the way to come to phrases with what physicists are asserting with an analogous phrases we use, yet with an ostensibly diversified that means. The ebook is really easy to learn, very common, jam-packed with examples...and workouts, and should do the task the writer wishes it to do with style.”

—MAA Reviews

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Example text

If S is not linearly dependent, then we say it is linearly independent, and in this case no vector in S can be written as a linear combination of any others. 0; 1; 1/g is linearly independent, as you should check. With these definitions in place we can now define a basis for a vector space V as an ordered linearly independent set B V whose span is all of V . This means, roughly speaking, that a basis has enough vectors to “make” all of V , but no more than that. When we say that B D fv1 ; : : : ; vk g is an ordered set we mean that the order of the vi is part of the definition of B, so another basis with the same vectors but a different order is considered distinct.

Vjw/. 7 Non-degenerate Hermitian Forms and Dual Spaces 41 where in the third equality we used the Hermiticity of our non-degenerate Hermitian form. A word of warning here: as a map from V ! v/ in the range of L is a dual vector, hence a fully linear map from V ! C . 21 below you will show that the non-degeneracy of . j / implies that L is one-to-one and onto, so L is an invertible map from V to V . This allows us to identify V with V , a fact we will discuss further below. 21. Use the non-degeneracy of .

E. addition and scalar multiplication are done component-wise. C/, which can of course be taken to be a complex vector space. You can again check that the axioms are satisfied. Though these vector spaces don’t appear explicitly in physics very often, they have many important subspaces, one of which we consider in the next example. 4. C/, so the commutativity of addition and the distributivity of scalar multiplication over addition follow immediately. C/ is closed under addition and contains the zero “vector” (in this case, the zero matrix), both of which are easily verified.

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