p09fl39 - Lecture 39: Electrodynamics (4 Dec 09) Project: 2...

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Unformatted text preview: Lecture 39: Electrodynamics (4 Dec 09) Project: 2 homework-like problems from Fetter-Walecka or Goldstein on under-represented topics in the homework, for instance Hamilton-Jacobi theory, continuum mechanics, hydrodynamics, or relativity. Due last class day (Dec 14). A. Review 1. The Lorentz transformation along x is ct * = ( ct- x ); x * = ( x- ct ) y * = y ; z * = z ; = v/c ; = 1 / q 1- 2 2. This is a special case of transformations on 4-vector x = ( ct, r ) pre- serving the length r 2- x 2 . ( g =- 1 ,g 1 = g 2 = g 3 = 1) x * = X a x ; ( x ,x ) X g x 2 ( x ,x ) = ( x * ,x * ) for matrices a , satisfying X g a a = g ; a- 1 = g g a 3. A 4-vector transforms as A * = X a A Some examples x = ( ct, r ), k = ( /c, k ), j = ( c, j ), 2 = g /x , p = ( E/c, p ). 4. The scalar products of two 4-vectors is a Lorentz invariant: ( A ,B ) X g A B and ( 2 , 2 ) is the wave equation operator; ( 2 ,j ) = 0 is the equation...
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p09fl39 - Lecture 39: Electrodynamics (4 Dec 09) Project: 2...

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