Final Report Summary - NCD OF QFT (Non-commutative deformations of quantum field theory) The project fully reached its goal of establishing models of deformed symmetries and curved momentum space as a promising area of research at the interface of quantum theory and gravity. The main focus was on those theories in which space-time coordinates form a Lie algebra, since similar structures are encountered in the description of "topologically" gravitating particles in three space-time dimensions. The main technical challenges in that context but also the main opportunities for significant discoveries reside in their group-valued plane waves and their relativistic symmetries deformed in the sense that the action of generators of Lorentz transformations on momentum space is non-linear and non-symmetric on products of plane waves. Among the outcomes of the project of particular significance are the ones concerning the conceptual connections of scenarios with curved momentum space and deformed relativistic symmetries with models exhibiting dimensional reduction at superPlanckian energy scales. Of comparable significance was the realization that the framework of deformed relativistic symmetries, at the quantum level, can account for a deformed evolution of density matrices which, in principle, allows the evolution of pure states into mixed states, opening a new window on the theoretical study of fundamental departures from unitary quantum evolution, with high potential of impact for the phenomenological searches for quantum gravity effects and for our understanding of the quantum evolution of black holes. Arzano also performed very well in supervising thesis students, as shown perhaps most notably by the results obtained by Arzano in collaboration with two of his Sapienza-University thesis students (the students D. Latini and M. Lotito) establishing fully a link between topological defects and relativistic-symmetry deformation in the context of three dimensional gravity. The significance of the scientific results is testified not only by prestigious publications and citations, but also by a second-place prize awarded by the Gravity Research Foundation for 2015. Moreover, an essay by Arzano was awarded the fourth-place prize in the essay contest "Questioning the foundations" hosted by the Foundational Questions Institute. The integration of Arzano was also rather successful, particularly in light of the fact that he obtained the habilitation for associate professorship in theoretical physics by the Italian Ministry of Education. He will continue to be employed by Sapienza University for at least two years after the end of the project.
