Topics in Real-Time Finite Temperature Field Theory.

After a review of the motivations and methods of finite temperature field theory we study two topics. The first one is the behavior of two point Green's functions at finite temperature near zero momentum. We show that, when properly evaluated, the finite temperature Green's functions of some theories are not smooth around this point. The condition for this to happen at the one loop level is that the particles in this loop should have the same mass. We analyze in detail models in which this does and does not occur. In the course of this analysis we clarify a few calculational details involving singular functions. The second topic is the non equilibrium dynamics of quantum fields during phase transitions. We concentrate on a model sudden quench of a QCD using a plasma and the subsequent chiral phase transition. The motivation is the possibility of the formation of disoriented chiral condensates in heavy ion collisions. We calculate the size of the correlated domains of the order parameter and the character of its evolution at large times. The way this result is obtained suggests that the large time evolution law should be largely independent of the specific model we consider.