using the Schwinger Dyson equations that gives us a differential expression for the functional Z[J] so Z[0] is just the path integral over 4-dimensional spaces .then for Einstein equation (no matter) they read (system of 10 functional equations)(adsbygoogle = window.adsbygoogle || []).push({});

[tex] R _{a,b}( -i \frac{ \delta Z (J)}{\delta J})+ J(x)Z(J)=0 [/tex]

then let's suppose we had a super-powerfull computer so we could solve these S-D equations Numerically could it be a solution to the problem of QG ?? , in fact could someone say me what methods are used to solve these kind of equations with functional derivatives ?? .. if possible in the perturbative and Non-perturbative expansions, thanks

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# Schwinger-Dyson equations for Quantum Gravity

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