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Make sure the Lagrangian symmetry?

  1. Jun 26, 2010 #1
    Is the Lagrangian of the neutral Proca field
    [tex]\mathcal{L}=-\frac{1}{16\pi}\left(F^{\mu\nu}F_{\mu\nu}-2m^2 A_{\mu} A^{\mu}\right)[/tex]
    And How to make sure whether it's symmetric.
  2. jcsd
  3. Jun 26, 2010 #2
    Symmetric in what?

  4. Jun 27, 2010 #3
    I mean if the Stress-energy momentum has the form [tex]T_{\mu\nu}=T_{\nu\mu}[/tex]
  5. Jun 30, 2010 #4


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    Well, take the functional derivative with respect to the metric of this Lagrangian. What do you get?

    If the EM-tensor is not symmetric, you can construct the so-called Belinfante tensor; see for instance DiFrancesco's "Conformal Field Theory", 2.5.1 :)
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