By Nadir Jeevanjee
The moment version of this hugely praised textbook presents an advent to tensors, workforce conception, 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 good points, akin to new illustrations, tables, and boxed sections, in addition to extra “invitation” sections that supply obtainable 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 workforce conception, 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 solid perform in making use of the awarded fabric and techniques.
Prerequisites for this article contain the normal lower-division arithmetic and physics classes, even though wide references are supplied for the prompted 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 ebook that may aid different physicists comprehend these topics [tensors and teams] as mathematicians comprehend them… From the 1st pages, Jeevanjee indicates outstanding ability to find clean, compelling phrases to carry ahead the perception that animates the fashionable 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 provides accepted instances with a freshness that may attract and reassure even a apprehensive scholar. [This] is a masterpiece of exposition and rationalization that may win credits for even a professional author.”
"Jeevanjee’s [text]is a necessary piece of labor on a number of counts, together with its show 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 a similar phrases we use, yet with an ostensibly varied which means. The booklet is really easy to learn, very easy, choked with examples...and workouts, and may do the activity the writer desires it to do with style.”
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Extra info for An Introduction to Tensors and Group Theory for Physicists
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. /, or equivalently . j /. 24. Raising and lowering indices in relativity Consider R4 with the Minkowski metric, let B D fe g D1;:::;4 and B D fe g D1;:::;4 be the standard basis and dual basis for R4 (wePuse a Greek index to conform 4 4 with standard physics notation21), and let v D D1 v e 2 R .
After all, when does one come across a single vector space that has multiple different, useful inner products defined on it? In this example we will meet one such vector space, and find that we have met the different inner products on it through our study of differential equations in physics. R/ of polynomials in one real variable x, with real coefficients. x/ D c0 C c1 x C c2 x 2 C C cn x n ; where ci 2 R 8 i and n is arbitrary. It is straightforward to verify that with the usual addition and scalar multiplication of polynomials, this set is in fact a vector space.
More on this later. 7 See Hoffman and Kunze . 2 Span, Linear Independence, and Bases 19 For the second space CR , however, 1 does not span the space: scalar multiplying 1 by only real numbers cannot yield arbitrary complex numbers. To span the space we need a complex number such as i . The set f1; i g then spans CR since any z 2 C can be written as z D a 1 C b i , where a; b 2 R. Thus, CR is two-dimensional. What we see, then, is that even though C and CR are identical as sets, they differ in vector space properties such as their dimensionality.