ar X iv : h ep - p h / 03 02 21 0 v 1 2 4 Fe b 20 03 PROGRESS IN NONEQUILIBRIUM QUANTUM FIELD THEORY

The advent of relativistic heavy-ion collision experiments as well as rapid progress in cosmological observations triggered an enormous increase of interest in the dynamics of quantum fields out of equilibrium. Much progress has been achieved for systems close to thermal equilibrium using (non-)linear response techniques or with effective descriptions based on a separation of scales in the weak coupling limit. These methods provide an efficient description of the dynamics on sufficiently long time scales in their range of applicability. Major open questions for our theoretical understanding are currently highlighted by experimental indications of early thermalization in collision experiments starting from extreme nonequilibrium situations. They provide an important motivation to study the far-from-equilibrium dynamics of quantum fields and subsequent thermalization from first principles. There are few necessary ingredients to describe far-from-equilibrium quantum fields. Firstly, in contrast to close-to-equilibrium field theory, the initial density matrix can deviate substantially from thermal equilibrium. Fully equivalent to the specification of a density matrix is a description of the nonequilibrium initial conditions in terms of correlation functions. Secondly, nonequilibrium time evolution involves no other dynamics than the one dictated by the underlying quantum field theory. In particular, the dynamics can be conveniently obtained from the effective action Γ for given