Homework Help: Lorentz transformation in four dimensions of the electromagnetic tensor

1. Apr 9, 2010

Vincent_111

1. The problem statement, all variables and given/known data

Given: electromagnetic tensor F(superscript)uv:

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.)