- #1
Kevin_spencer2
- 29
- 0
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)
\mathcal L = \int dx^{4} \sqrt (-g) g^{ik}(\Gamma^{m}_{il}\Gamma^{l}_{km}-\Gamma^{l}_{ik}\Gamma^{m}_{lm})
from this and definition of 'Chrisstoffel symbols' the Lagrangian would be quadratic in the metric and its first derivatives , if we impose the constraint:
\mathcal{g}+1 =0 (does it has any physical meaning??)
and a Qadratic Lagrangian in the derivatives and fields can be evaluated by means of a Functional integral.
\mathcal L = \int dx^{4} \sqrt (-g) g^{ik}(\Gamma^{m}_{il}\Gamma^{l}_{km}-\Gamma^{l}_{ik}\Gamma^{m}_{lm})
from this and definition of 'Chrisstoffel symbols' the Lagrangian would be quadratic in the metric and its first derivatives , if we impose the constraint:
\mathcal{g}+1 =0 (does it has any physical meaning??)
and a Qadratic Lagrangian in the derivatives and fields can be evaluated by means of a Functional integral.
