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Energy-momentum tensor for electromagnetism

  1. Jan 1, 2013 #1
    1. The problem statement, all variables and given/known data
    Derive
    Tμν=FμλFνλ-1/4ημνFλθFλθ
    From
    [tex]\mathcal{L}=1/4F_{μν}F^{μν}+A_μJ^μ[/tex]

    2. Relevant equations

    Above

    3. The attempt at a solution
    The first term of the given equation and the second term of the equation to prove are i believe the same.i know, Jμ=[tex]\partial_νF^{μν}[/tex]
    But I need an explanation for the equivalence of the remaining term.
    Thank You
     
  2. jcsd
  3. Jan 1, 2013 #2

    dextercioby

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    1. In the absence of gravity T follows from L from the Noether theorem and the Belinfante symmetrization procedure.

    2. In the presence of gravity T follows from L directly (even without the coupling to charged scalar matter).

    Both parts are (advanced) textbook stuff in either of the 3 subjects: classical electrodynamics or classical/quantum field theory (1.), general relativity (2.)

    Was this helpful for you ? Either 1. or 2. should give you a starting point.
     
  4. Jan 1, 2013 #3
    Thanks but can you suggest a book or something where i can understand this better, a good explanatory text perhaps.
     
  5. Jan 2, 2013 #4

    dextercioby

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  6. Jan 2, 2013 #5
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