• Loop quantum gravity

It has been shown that discretization of General Relativity admit a geometric interpretation via the so-called twisted geometries, that differ from the Regge calculus because they lack of the shape- matching conditions. However it is still not clear whether or not they are full dynamical objects or just a kinematical arena and the dynamics will deal with a Regge-like geometry.

The main goal of the thesis is to investigate the dynamical arising of these conditions as secondary constraint in a simple twisted-geometries’ discretisation of a flat space-time, triangulated with the graph of a single 4- simplex. The stability procedure pointed out the presence of secondary constraints which are equivalent to the well-known shape-matching conditions.