A search for the improvement of the coupling of gravity to matter in the Spin-foam and Group Field Theories formalisms

Abstract

In the context of quantum gravity, several independent approaches have been developed and they surprisingly converge to the same formalism, nowadays called Spin-foam formalism. This is a tentative co-variant formulation of transition amplitudes for quantum gravity which can be seen as a discretization of the path integral formalism introduced by Stephen Hawking, also known as sum-over-geometries. The Spin-foam formalism has attracted much interest recently because it aims to provide computational means to study and make predictions in the non-perturbative quantum gravity approach. A different point of view, named as Group Field Theories, emerged as a generalization of matrix models from 2-dimensional space-time to 3 and 4 space-time dimensions in order to reproduce a lattice formulation of topological theories. This new formalism culminated as an important procedure to describe any Spin-foam model as a Feynman amplitude of some Group Field Theory. Moreover, it is expected to obtain, when fully developed, a formalism which overcomes the main difficulties of some non-perturbative quantum gravity approaches, for example Loop Quantum Gravity and simplicial quantum gravity, and also provides a unifying language for them as a fundamental formulation of quantum gravity. Both formalisms, Spin-foam and Group Field Theories, are under research, among other things, to describe the coupling of matter with gravity at the quantum level. This line of research is still widely open, with many aspects to be unraveled. Then our main objective is to develop research on the coupling of gravity with gauge fields. Our point of departure will be the study of standard lattice gauge theory aiming the construction of local gauge fields out of Wilson loops. Moving to the framework of simplicial and Spin-foam quantum gravity we aim to improve the coupling of gravity to matter in this context and also use Group Field Theories to search a good definition for excitations of local quantum gravity over a geometric background. Moreover, if time is available, it will be interesting to look for a convincing Group Field Theory which includes the coupling of gravity with a scalar field in 4 dimensions.