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Nov 13, 2019 · Mathematicians represent these fields using an approach called index notation. ... physicists have developed a range of tools known as operators — perhaps the most famous being the del operator.

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In index notation, then, we have [L j;H D] = i[ jk‘r kp ‘;a ip i] = ia i[ jk‘r kp ‘;p i]: (35.10) Evaluating the right-hand side is straightforward, keeping in mind that in our current units, [r i;p j] = i ij, we have ia i[ jk‘r kp ‘;p i] = ia i jk‘(r kp ‘p i p ir kp ‘) = ia i jk‘(i ikp ‘+ p ir kp ‘ p ir kp ‘) = a i ji‘p ‘; (35.11) so that [L j;H D] = ji‘a

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The purpose of this problem is to get you used to index notation and in particular to 4-vector notation. Recall that the electric and magnetic ﬁelds can be derived in terms of two quantities, the scalar potential Φ and the vector-potential A~. It is also convenient to replace the magnetic ﬁeld with the antisymmetric 2-tensor Fij deﬁned as1

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To Anonymous: you ask in a comment "Without using index notation, is it possible to prove the identity?" Yes, it is possible, but at the sacrifice of rigor.

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In an expression, it has the e ect of replacing one index with another (remember the implicit summation): ijuj= ui The Kronecker- can be thought of as the identity matrix, e.g. in three dimen-sions ij= 2 4 0 @ 1 0 0 0 1 0 0 0 1 1 A 3 5 ij: The -tensor is rank{3, and is de ned by: ijk= 8 >< >: 1 ijkeven 1 ijkodd 0 otherwise:

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In this tutorial you'll learn how to use Python's rich set of operators, functions, and methods for working with strings. You'll learn how to access and extract portions of strings, and also become familiar with the methods that are available to manipulate and modify string data in Python 3.