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Variation of a tensor expression with indices

  1. Jun 12, 2015 #1
    Say I want to find ##\delta \bigg( \sqrt{- \eta_{\mu \nu} \frac{dx^{\mu}}{d \tau} \frac{dx^{\nu}}{d \tau}} \bigg)##.

    Is the following alright: ##\delta \bigg( \sqrt{- \eta_{\mu \nu}} \bigg( \frac{dx^{\mu}}{d \tau} \bigg)^{-1/2} \bigg( \frac{dx^{\nu}}{d \tau} \bigg)^{1/2} \bigg)##?
     
  2. jcsd
  3. Jun 12, 2015 #2

    Orodruin

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    No. You have broken out terms of a sum and it is no longer clear what is being summed with what. I suggest you use the chain rule ##\delta f(x) = f'(x) \delta x##.
     
  4. Jun 12, 2015 #3
    Thanks! I've got it.
     
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