Real-time dynamics of thermal field theories at intermediate coupling

The goal of ultrarelativistic heavy-ion collisions is to generate energy densities and temperatures high enough to create a plasma of quarks and gluons called the quark-gluon plasma. For heavy-ion experiments to have the greatest possible impact on scienc e, it is essential to make as close a connection to the fundamental theory of QCD as possible. There is an urgent need for theoretical analysis that is based rigorously on QCD but which can also make contact with more phenomenological approaches, particul arly in the area of equilibrium and non-equilibrium dynamics of QCD at intermediate coupling. Transport coefficients, such as the heavy quark diffusion, plasma viscosity, and jet transport, are of great interest along the research line since they are theo retically clean and well defined non-equilibrium dynamical quantities. Unfortunately, at finite-temperature naively resummed perturbation theory shows very poor convergence for both thermodynamics and non-equilibrium dynamics. It is clear that a reorganiz ation of the perturbation series is essential if perturbative calculations are to be of any quantitative use at temperatures accessible in heavy-ion collisions. Among varies resummation schemes, hard-thermal-loop perturbation theory (HTLpt) is a systemati c and gauge invariant reorganization of the conventional perturbation expansion for QCD that selectively resums higher order effects related to quasiparticles and screening. It has been shown through recent three-loop calculations that HTLpt improves the convergence of thermodynamic quantities dramatically compared to naively resummed perturbation theory. HTLpt is formulated in Minkowski space, so its application to non-equilibrium dynamics is straightforward. Therefore I propose generalizing HTLpt to rea l-time dynamics and the systematic application of HTLpt to non-equilibrium yields gauge-invariant infrared-safe results for observables which otherwise would be plagued by infrared divergences and gauge variance.