Generalized Ashtekar variables for Palatini f(R) models

We consider special classes of Palatini f(R) theories, featured by additional Loop Quantum Gravity inspired terms, with the aim identifying a set modified Ashtekar canonical variables, which still preserve SU(2) gauge structure standard theory. In particular, we allow for affine connection to be endowed torsion, turns out depend on scalar degree affecting gravity, and in this respect successfully construct novel Gauss constraint. analyze role field, outlining as it acquires dynamical character virtue non vanishing Immirzi parameter, describe some possible effects area operator stemming from such revised theoretical framework. Finally, compare our results earlier studies literature, discussing differences between metric approaches. It is worth noting how Hamiltonian different two cases. The can reconciled when analysis performed Einstein frame.