Low energy limit in Loop Quantum Gravity

In this doctoral thesis I developed techniques for the study of the low energy limit in Loop Quantum Gravity. Loop Quantum Gravity is a strong candidate theory for the non-perturbative quantization of the gravitational field. Though is unlikely that an experimental verification could be feasible in the next future, one can at least try to recover the correct semiclassical limit of the theory. First of all, the leading order of the 2-point function computed in LQG should reproduce the Newtonian potential in the large distance regime; more in general, the n-point functions of LQG should match with the n-point functions computed in conventional quantum field theory of gravitons. An origianal contribution to the calculation of the graviton propagator in LQG is presented. A second approach to the semiclassical limit is introduced for the first time in this thesis, and it is based on the coherent propagation of semiclassical wavepackets. Both approaches to the analysis of the dynamical sector of LQG are covered extensively.