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 ˆ x is ct * = γ ( ct- βx ); x * = γ ( x- βct ) y * = y ; z * = z ; β = v/c ; γ = 1 / q 1- β 2 2. This is a special case of transformations on 4-vector x μ = ( ct, r ) pre- serving the length r 2- x 2 . ( g =- 1 ,g 1 = g 2 = g 3 = 1) x * μ = X ν a μν x ν ; ( x μ ,x μ ) ≡ X μ g μ x 2 μ ( x μ ,x μ ) = ( x * μ ,x * μ ) for matrices a μ,ν satisfying X μ g μ a μν a μλ = g ν δ νλ ; a- 1 νμ = g ν g μ a μν 3. A 4-vector transforms as A * μ = X ν a μν A ν Some examples x μ = ( ct, r ), k μ = ( ω/c, k ), j μ = ( cρ, j ), 2 μ = g μ ∂/∂x μ , p μ = ( E/c, p ). 4. The scalar products of two 4-vectors is a Lorentz invariant: ( A μ ,B μ ) ≡ X μ g μ A μ B μ and ( 2 μ , 2 μ ) is the wave equation operator; ( 2 μ ,j μ ) = 0 is the equation...
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This note was uploaded on 12/14/2009 for the course PHYS 711 taught by Professor Bruch during the Fall '09 term at University of Wisconsin.

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

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