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

By Nadir Jeevanjee

ISBN-10: 0817647147

ISBN-13: 9780817647148

An advent to Tensors and staff conception for Physicists offers either an intuitive and rigorous method of tensors and teams and their position in theoretical physics and utilized arithmetic. a selected goal is to demystify tensors and supply a unified framework for figuring out them within the context of classical and quantum physics. Connecting the part formalism widespread in physics calculations with the summary yet extra conceptual formula present in many mathematical texts, the paintings can be a great addition to the literature on tensors and workforce theory. Advanced undergraduate and graduate scholars in physics and utilized arithmetic will locate readability and perception into the topic during this textbook.

Show description

Read Online or Download An Introduction to Tensors and Group Theory for Physicists PDF

Best linear books

Download e-book for kindle: Banach lattices by Peter Meyer-Nieberg

This e-book is worried basically with the idea of Banach lattices and with linear operators outlined on, or with values in, Banach lattices. extra common sessions of Riesz areas are thought of as long as this doesn't bring about extra advanced buildings or proofs. The intentions for penning this ebook have been twofold.

Nanhua Xi's Representations of Affine Hecke Algebras PDF

Kazhdan and Lusztig categorized the easy modules of an affine Hecke algebra Hq (q E C*) only if q isn't a root of one (Invent. Math. 1987). Ginzburg had a few very fascinating paintings on affine Hecke algebras. Combining those effects uncomplicated Hq-modules might be categorised only if the order of q isn't really too small.

Download e-book for iPad: Linear Agebra and Its Applications by Gilbert Strang

Popular professor and writer Gilbert Strang demonstrates that linear algebra is an interesting topic by means of displaying either its attractiveness and cost. whereas the maths is there, the trouble isn't all targeting proofs. Strang's emphasis is on figuring out. He explains ideas, instead of deduces. This ebook is written in an off-the-cuff and private variety and teaches genuine arithmetic.

New PDF release: A Course in Linear Algebra

Appropriate for complex undergraduates and graduate scholars, this article bargains a whole advent to the elemental suggestions of linear algebra. attention-grabbing and encouraging in its technique, it imparts an knowing of the subject's logical constitution in addition to the ways that linear algebra presents options to difficulties in lots of branches of arithmetic.

Extra resources for An Introduction to Tensors and Group Theory for Physicists

Example text

20) 26 2 Vector Spaces where δji is the usual Kronecker delta. If V is finite-dimensional with dimension n, it is then easy to check (by evaluating both sides on basis vectors) that we can write14 n f= fi e i i=1 so that the fi really are the components of f . Since f was arbitrary, this means that the ei span V ∗ . ,n is actually a basis for V ∗ . We sometimes say that the ei are dual to the ei . Note that we have shown that V and V ∗ always have the same dimension. We can use the dual basis {ei } ≡ B ∗ to write f in components, ⎛ ⎞ f1 ⎜ f2 ⎟ ⎜ ⎟ [f ]B∗ = ⎜ .

28) Aij Notice that the components of v transform with the whereas the basis vectors j transform with the Ai , so the components of a vector obey the law opposite (‘contra’) to the basis vectors. This is the origin of the term ‘contravariant’. Note also that the components of a dual vector transform in the same way as the basis vectors, hence the term ‘covariant’. It makes sense that the basis vectors and the components of a vector should transform oppositely; v exists independently of any basis for V and should not change under a change of basis, so if the ei change one way the v i should change oppositely.

And vn ⎜ ⎜ T (v) B = ⎜ ⎜ ⎝ n i 1⎞ i=1 v Ti n i 2⎟ i=1 v Ti ⎟ .. ⎟, ⎟ ⎠ n i n i=1 v Ti which looks suspiciously like matrix multiplication. In fact, we can define the matrix of T in the basis B, denoted [T ]B , by the matrix equation T (v) B = [T ]B [v]B where the product on the right-hand side is given by the usual matrix multiplication. Comparison of the last two equations then shows that ⎛ 1 ⎞ T1 T 2 1 . . Tn 1 ⎜T 2 T 2 ... 15) .. .. ⎟ . ⎜ .. ⎝ . . ⎠ T1 n T2 n . . Tn n Thus, we really can use the components of T to represent it as a matrix, and once we do so the action of T becomes just matrix multiplication by [T ]B !

Download PDF sample

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

by Charles

Rated 4.14 of 5 – based on 24 votes