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Four momentum vector from energy-momentum-tensor

  1. Jul 28, 2009 #1
    for a real scalar field one has the energy momentum tensor from Noethers theorem
    [tex]T^{\mu\nu} = \frac{\partial \mathcal{L}}{\partial \partial_\mu \phi} \partial^\nu \phi - \eta^{\mu\nu} \mathcal{L} [/tex]
    and the conserved quantities
    [tex]P^\nu = \int d^3 x \ T^{0\nu}[/tex]

    Now, how can one show that P is really a 4-vector, since the definition looks not that covariant and I could not think of anything.

    Thanks for your response,
  2. jcsd
  3. Jul 28, 2009 #2


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  4. Jul 29, 2009 #3
    Ah, thanks a lot.
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