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Einstein action.

  1. Jan 25, 2007 #1
    In Landau's bok "Classical Field Theory" pages: 372-373-374 they manage to get the Einstein-Hilbert action (after integrating by parts and use divergence theorem)

    [tex] \mathcal L = \int dx^{4} \sqrt (-g) g^{ik}(\Gamma^{m}_{il}\Gamma^{l}_{km}-\Gamma^{l}_{ik}\Gamma^{m}_{lm}) [/tex]

    from this and definition of 'Chrisstoffel symbols' the Lagrangian would be quadratic in the metric and its first derivatives , if we impose the constraint:

    [tex] \mathcal{g}+1 =0 [/tex] (does it has any physical meaning??)

    and a Qadratic Lagrangian in the derivatives and fields can be evaluated by means of a Functional integral.
     
  2. jcsd
  3. Jan 26, 2007 #2

    Mentz114

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    Gold Member

    Please clean up and edit. The last formula makes no sense.
     
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