Field theory for hydrodynamics and strong gauge theory dynamics

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Quantum Chromodynamics (QCD) is our theory of the strong interactions which hold together the atomic nucleus. Our standard theoretical tool for making predictions in QCD, perturbation theory, fails when trying to study the dynamics of ultra-high temperature systems, like what existed in the early Universe and what we can now create in the lab via high energy heavy ion collisions. I will study ways to make theoretical predictions which improve on perturbation theory. One avenue of attack will be a way to improve perturbation theory called "resummation." Specifically I will study the 3-loop, 3-particle irreducible resummation of nonabelian gauge theories (such as QCD). As a warmup I will first study the theory in 3 dimensions, where the resummation method can be systematically tested; if it works I will attempt to apply it in the physical 3 space + 1 time dimensions. In addition, I will investigate the systematics of another approach which avoids the need for perturbation theory altogether -- relativistic hydrodynamics. Hydrodynamic studies have shown that the Quark-Gluon Plasma created by heavy ion collisions is the "most perfect" fluid known, in the sense of having the lowest viscosity when measured in appropriate units. I want to help quantify that and to figure out exactly how self-consistent and reliable the hydrodynamic treatment is.