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## Main Question or Discussion Point

**GR as a Gauge theory ??**

don't know if this is true or not, but i have been reading books by ROvelli (LQG) or 'Gauge theories' the question is could we study Gravity as the set of functions [tex] A_{\mu}^{I}(x) [/tex]

Then we write the Einstein Lagrangian (or similar) as:

[tex] \mathcal L = F_{ab}^{I}F^{I}_{ab} [/tex] (sum over I=0,1,2,3)

[tex] F_{ab}= \partial _{a}A^{I}_{b}-\partial _{b}A^{I}_{a}-\Gamma_{jk}^{i}A_{j}^{I}(x) A_{k}^{I}(x) [/tex]

I think Rovellli in his LQG theory used this representation... then [tex] (\partial_{0}A_{\mu}^{I} [/tex] is the Kinetic part of Lagrangian and

[tex] dA_{\mu}^{I} [/tex] (d- exterior derivative) represents the potential.

then how would it read the Einstein Field equation and the Riemann or similar tensors ??