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Variation of quadratic action

  1. Aug 27, 2010 #1
    Do know anybody explicit form of variation action quadratic in Riemann tensors (for general dimension)?
    Link to internet sources?
    Or computer program for symbolic and tensors algebra, which the variation tell me (preferably open-source)?

  2. jcsd
  3. Aug 27, 2010 #2
    Hint: Write the curvature tensor as

    [tex]R_{\mu\nu}=\partial_\mu \Gamma_{\nu}-\partial_\nu \Gamma_{\mu}-[\Gamma_\mu,\Gamma_\nu][/tex]

    Then apply the variation [tex]\delta[/tex]. Use the Leibniz rule.
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