My master's thesis in LQG

This repository just contains the whole $\LaTeX$ project of my master's thesis at the University of Trento. I have been supervised by professor Lorenzo Fatibene of University of Torino, my work being based on a collection of 9 lecture notes of him, on the Loop Quantisation of Gravity (LQG), still in process of publication. The purpose of this work would be to provide the reader with a comprehensive mathematical self-consistent review of LQG, which is indeed pioneered by physicists.

At the end of that, the whole matter lands on a scenario where the (vacuum) physical space turns out to be, at a quantum level, a discrete kinematical object woven on a lattice made of 4-valence nodes with certain spin properties, being hence nothing but quantum tetrahedra that enclose all the geometric properties that one expects quanta of space to have. The gravitational field is so kinematical depicted quantumly by such spin tetrahedra representing its quantum states, within which one can measure areas, lengths, volumes, angles, by treating all these geometric features as quantum observables of a Poisson system modeling the classical tetrahedra geometries, in a perfect first-quantisation flavor.