PROCEEDINGS OF RIKEN/BNL RESEARCH CENTER WORKSHOP, EQUILIBRIUM AND NON-EQUILIBRIM ASPECTTS OF HOT, DENSE QCD, VOLUME 28.

The Relativistic Heavy Ion Collider (RHIC) at Brookhaven, beginning operation this year, and the Large Hadron Collider (LHC) at CERN, beginning operation {approximately}2005, will provide an unprecedented range of energies and luminosities that will allow us to probe the Gluon-Quark plasma. At RHIC and LHC, at central rapidity typical estimates of energy densities and temperatures are e * 1-10 GeV/fm3 and T0 * 300 - 900 MeV. Such energies are well above current estimates for the GQ plasma. Initially, this hot, dense plasma is far from local thermal equilibrium, making the theoretical study of transport phenomena, kinetic and chemical equilibration in dense and hot plasmas, and related issues a matter of fundamental importance. During the last few years a consistent framework to study collective effects in the Gluon-Quark plasma, and a microscopic description of transport in terms of the hard thermal (and dense) loops resummation program has emerged. This approach has the potential of providing a microscopic formulation of transport, in the regime of temperatures and densities to be achieved at RHIC and LHC. A parallel development over the last few years has provided a consistent formulation of non-equilibrium quantum field theory that provides a real-time description of phenomena out of equilibrium. Novel techniques including non-perturbative approaches and the dynamical renormalization group techniques lead to new insights into transport and relaxation. A deeper understanding of collective.excitations and transport phenomena in the GQ plasma could lead to recognize novel potential experimental signatures. New insights into small-c physics reveals a striking similarity between small-c and hard thermal loops, and novel real-time numerical simulations have recently studied the parton distributions and their thermalizations in the initial stages of a heavy ion collision