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Homework Help: Electromagnetic Lagrangian, EoM, Polarisation States

  1. Dec 8, 2017 #1
    1. The problem statement, all variables and given/known data

    Attached:

    queey.png
    2. Relevant equations

    Euler-Lagrange equations to find the EoM

    3. The attempt at a solution

    Solution attached:

    solly.png

    I follow, up to where the sum over ##\mu## reduces to sum over ##\mu=i## only, why are there no ##\mu=0## terms? I don't understand at all.

    Many thanks
     
  2. jcsd
  3. Dec 8, 2017 #2

    TSny

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    According to equation (9), what can you say about ##F_{00}##? What does this tell you about ##F^{00}##?
     
  4. Dec 9, 2017 #3
    oh for a antisymmetric tensor all diagonal entries must be zero? ##F_{ii}=0 ## as is ##F_{00} ##?
     
  5. Dec 9, 2017 #4

    TSny

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    Yes. The expression for ##F_{\mu \nu}## in (9) shows that ##F## is antisymmetric. In particular, if you let ##\mu = 0## and ##\nu = 0## in the expression for ##F_{\mu \nu}## in (9) then you see that ##F_{00} = 0##.
     
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