Quantum field kinetics of QCD: quark-gluon transport theory for light-cone dominated processes

A quantum kinetic formalism is developed to study the dynamical interplay of quantum and statistical-kinetic properties of non-equilibrium multi-parton systems produced in high-energy QCD processes. The approach provides the means to follow the quantum dynamics in both space-time and energy-momentum, starting from an arbitrary initial configuration of high-momentum quarks and gluons. Using a generalized functional integral representation and adopting the `closed-time-path' Green function techniques, a self-consistent set of equations of motions is obtained: a Ginzburg-Landau equation for a possible color background field, and Dyson-Schwinger equations for the 2-point functions of the gluon and quark fields. By exploiting the `two-scale nature' of light-cone dominated QCD processes, i.e. the separation between the quantum scale that specifies the range of short-distance quantum fluctuations, and the kinetic scale that characterizes the range of statistical binary inter- actions, the quantum-field equations of motion are converted into a correspon- ding set of `renormalization equations' and `transport equations'. The former describe renormalization and dissipation effects through the evolution of the spectral density of individual, dressed partons, whereas the latter determine the statistical occurrence of scattering processes among these dressed partons. The renormalization equations and the transport equations are coupled, and hence must be solved self-consistently. This amounts to evolving the multi-parton system, from a specified initial configuration, in time and full 7-dimensional phase-space. This description provides a proba- bilistic interpretation and is therefore of important practical value for the solution of the dynamical equations of motion, e.g. by Monte Carlo simulation.