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

By Nadir Jeevanjee

The moment variation of this hugely praised textbook presents an creation to tensors, staff idea, and their purposes in classical and quantum physics. either intuitive and rigorous, it goals to demystify tensors via 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 beneficial properties, corresponding to new illustrations, tables, and boxed sections, in addition to extra “invitation” sections that offer obtainable introductions to new fabric, provide elevated visible engagement, readability, and motivation for students.

Part I starts off with linear algebraic foundations, follows with the fashionable component-free definition of tensors, and concludes with purposes to physics by utilizing tensor items. half II introduces crew concept, together with summary teams and Lie teams and their linked Lie algebras, then intertwines this fabric with that of half I via introducing illustration conception. Examples and workouts are supplied in each one bankruptcy for sturdy perform in utilising the awarded fabric and techniques.

Prerequisites for this article comprise the normal lower-division arithmetic and physics classes, notwithstanding huge references are supplied for the stimulated pupil who has no longer but had those. complex undergraduate and starting graduate scholars in physics and utilized arithmetic will locate this textbook to be a transparent, concise, and interesting advent to tensors and groups.

**Reviews of the 1st Edition**

“[P]hysicist Nadir Jeevanjee has produced a masterly publication that would aid different physicists comprehend these matters [tensors and teams] as mathematicians comprehend them… From the 1st pages, Jeevanjee indicates extraordinary ability to find clean, compelling phrases to convey ahead the perception that animates the fashionable mathematical view…[W]ith compelling strength and readability, he presents many rigorously worked-out examples and well-chosen particular difficulties… Jeevanjee’s transparent and forceful writing offers prevalent instances with a freshness that might attract and reassure even a worried pupil. [This] is a masterpiece of exposition and rationalization that will win credits for even a professional author.”

—Physics Today

"Jeevanjee’s [text]is a worthy piece of labor on numerous counts, together with its exhibit pedagogical carrier rendered to fledgling physicists and the truth that it does certainly supply natural mathematicians how to come to phrases with what physicists are asserting with an analogous phrases we use, yet with an ostensibly diversified which means. The ebook is so easy to learn, very basic, filled with examples...and routines, and should do the activity the writer desires it to do with style.”

—MAA Reviews

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**Extra info for An Introduction to Tensors and Group Theory for Physicists**

**Sample text**

13. Let . j / be an inner product. e. ei jej / D 0 when i ¤ j , show that they are linearly independent. ei jej / D ˙ıij ) is just an orthogonal set in which the vectors have unit length. 14. Let v; v 0 be two nonzero vectors in V . v 0 jw/ 8 w 2 W , then condition 3 above is violated. 18. w1 ; : : : ; wn / 2 Rn . Define . vjw/ Á n X v i wi : i D1 This is sometimes written as v w. You can check that . 8 is an orthonormal basis. 19. w1 ; : : : ; wn / 2 Cn . Define . 30) i D1 Again, you can check that .

What, exactly, are they? Most quantum mechanics texts gloss over their definition, just telling us that they are in 1–1 correspondence with kets and can be combined with kets as h j i to get a scalar. e. that the bra corresponding to cj i is ch N j. From what we have seen in this section, then, we can conclude the following: Bras are nothing but dual vectors. These dual vectors are labeled in the same way as regular vectors, because the map L allows us to identify the two. In short, h j is really just L.

In fact, these linear functionals just eat a function and spit out its nth Fourier coefficient. 29) Note the similarity, in that both are used to evaluate arbitrary functions at 0. Later, in Sect. x/ and its relationship to the Dirac delta functional ı, as well as prove that ı can’t be written as a linear combination of the e i . 6 Non-degenerate Hermitian Forms Non-degenerate Hermitian forms, of which the Euclidean dot product, Minkowski metric, and Hermitian scalar product of quantum mechanics are but a few examples, are very familiar to most physicists.