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Lorentz transformation in four dimensions of the electromagnetic tensor

  1. Apr 9, 2010 #1
    1. The problem statement, all variables and given/known data

    Given: electromagnetic tensor F(superscript)uv: f98c8024db68e152f96a645328875fb5.png

    electromagnetic tensor F' after the lorentz transformation:
    [ 0 -Ex -gamma(Ey-VBz/c) -gamma(Ez-VBy/c)
    Ex 0 -gamma(Bz-VEy/c) gamma(By-VEz/c)
    gamma(Ey-VBz/c) gamma(Bz-VEy/c) 0 -Bx
    gamma(Ez-VBy/c) -gamma(By-VEz/c) Bx 0]

    Problem statement: "provide the an (theoretical) explanation and show the intermediate steps in the transformation from F to F'."


    2. Relevant equations

    E (electric field) = -grad (electric potential) - 1/c dA/dt
    B (magnetic field = rot A
    Transformation law of a tensor(in formal notation): F'uv (superscript) = A u(sup.scpt) a(sub. scrpt) A v(sup)b(sub) F ab (sup)


    3. The attempt at a solution

    The transformation has to do with the reletive direction+speed(?) of the second frame and I suppose we could take a 'simple' transformation in which we move from a 'rest frame' to a frame that moves with constant speed along the x-axes, which would yield relatively simple matrices.

    I am however unsure how we can construct the two matrices;
    A u(sup) a(sub) and
    A v(sup) b(sub)

    Could anyone make any sense of this or comment on things that are not clear, I would appriciate it

    PS: (I apologize for the weird notations I am not able to produce formulas with the program on my computer at this instant.)
     
  2. jcsd
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