# GR as a Gauge theory ?

## 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 $$A_{\mu}^{I}(x)$$

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

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

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

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

$$dA_{\mu}^{I}$$ (d- exterior derivative) represents the potential.

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