Scientific Activity

In the last years I have mostly worked on Out-of-Equilibrium Quantum Field Theory and its applications. Out-of-Equilibrium QFT is especially needed in the study of the Early Universe Physics and in Heavy Ion collisions since in these situations the time evolution of the system is so rapid that a local thermodynamical equilibrium assumption cannot hold; moreover a full relativistic treatment is needed. For sake of discussion, Out of Equilibrium QFT can be split into two different realms: the realm of systems strongly out of equilibrium and the realm of systems weakly of equilibrium. Both from the physical and the technical point of view, the two realms are very different and are studied with completely different tools. As it can be expected, strongly out of equilibrium systems are much more difficult to study and their analysis is at the very beginning. The systems where we have the most of information and understanding are simple systems containing scalar fields, like the $O(N)$ linear sigma-model which has been understood well enough in the large $N$ limit, or in similar frameworks such as the Hartree-Fock approximation, where the theory is gaussian-like [1], at least for homogeneous systems. The non-homogeneous situation is numerically challenging but within the reach of present day computers [3]. The study of next-to-leading corrections has been started very recently and it looks very promising [2]; the same can be said for what concerns even the leading order in $1/N$ for more complicate systems like Yukawa systems or quantum electrodynamics. On the other hand, much more has been understood in the case of weakly out of equilibrium systems, in which there are standardized methods to attack the problem. The fundamental tool to perform the study of weakly out of equilibrium systems is linear response theory. Consider a system near equilibrium, i.e. with a density matrix equal to a thermal density matrix except for a small disturbance, which can be imputed to the presence of a set of small external sources $J^i(x)$ coupled to the fundamental fields $\phi^i(x)$ of the system. The only non-equilibrium effects, neglecting quadratic effects in $J$, are in the evolution of one-point functions $<\phi^i(x)>_\rho$ and two-point functions $<\phi^i(x)\phi^j(y)>_\rho$. Since the density matrix is nearly thermal, methods of thermal field theory can be used and the evolution can be studied in principle by using perturbation theory, i.e. by computing thermal Feynman diagrams. The difficulties come from severe infrared divergences which invalidate naive perturbation theory and require resummation of infinite sets of diagrams. Eventually, under certain conditions, the effect of this resummation is believed to be equivalent to a phenomenological effective classical kinetic theory, based on a quantum-relativistic Boltzmann equation. However the precise correspondence within the classical theory and the underlying quantum field theory is not very well understood, except in the case of the $\phi^4$ theory [4]. In my work, I was particularly interested in studying situations under which the kinetic approximation fails, the approach to thermalization is subtle and non-equilibrium effects are expected to play a major role.