Kevin_spencer2
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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.
[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.