Affine gauge theory of gravity and its reduction to the Riemann-Cartan geometry

Abstract: We discuss a possible framework for the construction of a quantum gravity theory where the principles of QFT and general relativity can coexist harmonically. Moreover, in order to fix the correct gauge group of the theory we study the most general one, the affine group and its natural reduction to the orthogonal group. The price we pay for simplifying the geometry is the presence of matter fields associated with the nonmetric degrees of freedom of the original setup. The result is independent of the starting theory.