Nuclear/Riken Theory Committee

In this talk, I would like to start with a brief introduction to non-equilibrium quantum field theory in the Schwinger-Keldysh formalism. This formalism provides a systematic way to study isotropization and other time-dependent non-equilibrium (and equilibrium) phenomena in heavy-ion collisions. I shall first discuss the foundation of classical field approximations (CSA), which is an important tool to study the evolution at very early stages. It is, however, found to be non-renormalizable. This helps us understand better the applicability of such an approximation. it is now well-known that isotropization can not be established before the breakdown of the CSA. We then use another approximation, the quasi-particle approximation (the Boltzmann equation), to study the isotropization in a scalar field theory. Our result shows explicitly the importance of quantum effects. Motivated by these observations, we have been studying whether the isotropization can be reached before the dense system of gluons, produced in the collisions of two big nuclei, becomes too dilute to be studied perturbatively in the Schwinger-Keldysh formalism. Some preliminary results shall be reported.