Lagrangian and Hamiltonian formulations of the Palatini action

Abstract

We derive the Ashtekar-Barbero variables in Loop Quantum Gravity(LQG) starting from the Palatini action. We find that we need either the torsion-free condition or the compatibility condition for the Palatini action to describe General Relativity.

Comments: This paper is not understood as the author intended. I do not think it should be here anymore