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Homework Help: Relativity Mathematical Notation

  1. Dec 15, 2015 #1
    1. The problem statement, all variables and given/known data

    Find t(τ), x(τ), y(τ), z(τ) for constant electric field E=E(sinθx+cosθz) and B=Bz, and constant magnetic field where E,B, and θ are all constants.

    I haven't seen this notation before, and I really just want to know what it means specifically. I know and up indice paired with a down indice essentially gives an inner product, but I don't really know what an up indice paired with an up indice gives me. So this is equation 12.32 in Jackson Electrodynamics that I'm trying to understand.
    2. Relevant equations

    3. The attempt at a solution
    Also, the 4 vector potential that I've already calculated is:

    Aα=(-E(xsinθ+zcosθ),-By,0,0) where E, B and θ are all constants.

    or Aα=(-E(xsinθ+zcosθ),0,Bx,0) I can't decide which one is more convenient.

    I've attached an image of my best guess for what that equation means.

    Attached Files:

    Last edited: Dec 15, 2015
  2. jcsd
  3. Dec 15, 2015 #2
    I think its best to think of this way:

    Since beta is a free index, you get one equation for each value of beta (so you get 4 equations). In each of those equations, alpha is summed over (it is up for A and down for x). So each one of those equations can now be solved for the four functions you need.

    By the way for n free indicides in an equation in dimension d, you get d^n equations. In this case, d=4 and n=1
    Last edited: Dec 15, 2015
  4. Dec 16, 2015 #3


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    Just a small correction (I am sure it is a typo): it is alpha which is a free index and beta is summed over.
  5. Dec 17, 2015 #4
    Ohh thanks. Got them flipped xD
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