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Is a symmetric Lagrangian leads to a symmetric Stress-Energy Momentum?

  1. Jul 2, 2010 #1
    Is a symmetric Lagrangian leads to a symmetric Stress-Energy Momentum ?
     
  2. jcsd
  3. Jul 2, 2010 #2

    blechman

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    A "symmetric energy momentum tensor" obeys [itex]T_{\mu\nu}=T_{\nu\mu}[/itex].

    A Lagrangian is a scalar, with no indices.

    So what does one have to do with another?
     
  4. Jul 2, 2010 #3
    I was adoubt if a symmetric stress-energy tensor 's lagrangian is symmetry .

    Since [itex] {\cal L}= - \frac{1}{16\pi}F^{\mu\nu} F_{\mu\nu}[/itex] is symmetry on \mu &\nu,the corresponding Stress-Energy Tensor [itex]\Theta^{\mu}\,_{\nu} = - \frac{1}{4 \pi} F^{\mu \alpha} \partial_{\nu}A_{\alpha} + \frac{1}{16\pi} \delta^{\mu}_{\nu} F^{\alpha\beta}F_{\alpha\beta} [/itex] is also symmetry.

    Is this the special one ?
     
    Last edited: Jul 2, 2010
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