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Contractions of indices of the 4-vectors

  1. Oct 27, 2013 #1
    Hi, can someone confirm those or did I not get the meaning of the 4-vectors indices:

    [itex]\partial^{\mu}x_{\mu}=4;\partial^{\mu}x^{\mu}=2;\partial^{\mu}x_{\nu}= \delta ^{\mu}_{\nu};\partial^{\mu}x^{\nu}=g^{\mu\nu}[/itex]
  2. jcsd
  3. Oct 27, 2013 #2
    Those are all numerically correct, however the second one is not a valid tensor equation, because you have two raised [itex]\mu[/itex] indices. Correct tensor equations always have contractions between one upper and one lower index--if you don't do that, the resulting equation is not Lorentz-invariant.
  4. Oct 27, 2013 #3
    Thank you for the clarification
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