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Unformatted text preview: Lecture 39: Electrodynamics (4 Dec 09) Project: 2 homeworklike problems from FetterWalecka or Goldstein on “underrepresented topics” in the homework, for instance HamiltonJacobi 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 4vector 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 4vector 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 4vectors 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.
 Fall '09
 BRUCH
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