Ricerc@Sapienza

The theoretical challenge of making Quantum Field Theory and General Relativity work together takes the name of Quantum Gravity (QG). The search for QG is far form conclusion but it has led to several impressive proposals. However, in the absence of experimental hints, researches started wondering how QG can make progress. We believe that this can be possible if we: construct bridges between different approaches and quest for model-independent results. Reaching a synergy between top-down and bottom-up approaches would allow to obtain both guidance on the most significant formal structures and develop insight on how to handle those structures, hopefully also in terms of experimental tests. A contact point may reside in the modifications of the hypersurface deformation algebra (HDA), recently derived in loop quantum gravity (LQG). In fact, taking the Minkowski limit, those corrections give rise to a Deformed Special Relativity (DSR) scenario. We have found that this LQG-inspired DSR model describes the symmetries of a non-commutative spacetime. First, we aim to extend the domain of validity of these results. Then, encouraged by them, we wish to pursue an almost complementary path: deriving the HDA for non-commutative manifold. This represents a long-standing challenge, whose solution would impact on many fields of research such as string theory. Another strategy is to look for features that are shared by different QG programs. Among them, pride of place is held by the reduction of dimensions near the QG scale, as realised e.g. in multifractal and miltifractional models. Our objective is to investigate the relation of dimensional reduction with spacetime fuzziness, a feature that is directly inherited by the coexistence of quantum mechanical and general relativistic principles. Besides shedding light on the recurrence of dimensional flow in QG studies, establishing such a relation would open up the possibility to test QG running dimensions in uncertainty measurements.