Non-Equilibrium Dynamics of Phase Transitions: From the Early Universe to Chiral Condensates

In this brief review we introduce the methods of quantum field theory out of equilibrium and study the non-equilibrium aspects of phase transitions. Specifically we critically study the picture of the ``slow-roll'' phase transition in the new inflationary models, we show that the instabilities that are the hallmark of the phase transition, that is the formation of correlated domains, dramatically change this picture. We analyze in detail the dynamics of phase separation in strongly supercooled phase transitions in Minkowski space. We argue that this is typically the situation in weakly coupled scalar theories. The effective evolution equations for the expectation value and the fluctuations of an inflaton field in a FRW cosmology are derived both in the loop expansion and in a self-consistent non-perturbative scheme. Finally we use these non-equilibrium techniques and concepts to study the influence of quantum and thermal fluctuations on the dynamics of a proposed mechanism for the formation of disoriented chiral condensates during a rapid phase transition out of equilibrium. This last topic may prove to be experimentally relevant at present accelerator energies. To appear in the Proceedings of the `2nd. Journ\'ee Cosmologie', Observatoire de Paris, 2-4, June 1994. H J de Vega and N. S\'anchez, Editors, World Scientific.