Spin Foam Models for Quantum Gravity

This project is concerned with the problem of dynamics in the context of the theory of quantum gravity known as {\em loop quantum gravity} (LQG). LQG is a promising approach to the construction of a unified description of nature that would reconcile the principles of general relativity (governing gravitational phenomena at large scales) and the principles of quantum mechanics (governing material phenomena at microscopic scales). Important progress has been achieved in LQG leading to a simple understanding of the nature of the fundamental constituents of space and time. For example the theory predicts that space itself is discrete at the microscopic scales and constructed out of fundamental building blocks. Space is constituted by basic objects in a way that resembles the lattice structure of {\em atoms} in a crystalline material. My work aims at understanding the dynamics of these fundamental constituents, i.e., how they interact and evolve. This is an issue that remains unsolved to a large extend in the approach.

The effects of quantum gravity are expected to be important at the extremely small length scale

given by the Planck length. Understanding of phenomena in these regimes is very important for addressing issues concerning the physics of the early universe (why does the universe has evolved into what we see today?), the structure of space and time, and the physics of strong gravitational fields (e.g. near a black hole singularity) among other fundamental questions. Theoretical understanding would provide new insight into questions that are not apparent at present leading to experimental tests and possible applications in the future.