The NCD OF QFT (Non-commutative deformations of quantum field theory) project had as its goal to establish models of deformed symmetries and curved momentum space 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 challenge was to model 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 project's outcomes, of particular significance are those concerning the conceptual connections of scenarios with curved momentum space and deformed relativistic symmetries with models exhibiting dimensional reduction at super-Planckian energy scales. Also important was the realisation that the framework of deformed relativistic symmetries, at the quantum level, can account for a deformed evolution of density matrices. This allows the evolution of pure states into mixed states, opening a new window on the theoretical study of fundamental departures from unitary quantum evolution. There is high potential of impact for the phenomenological searches for quantum gravity effects and for our understanding of the quantum evolution of black holes. Results obtained in collaboration with two Sapienza University thesis students establish a link between topological defects and relativistic symmetry deformation in the context of three-dimensional gravity. The Gravity Research Foundation awarded a second place prize for this work in 2015. An essay also earned the fourth place prize in the essay contest 'Questioning the Foundations', hosted by the Foundational Questions Institute.
Quantum fields, gravity, quantum theory, NCD OF QFT, space-time, relativistic symmetries