Field theory for hydrodynamics and strong gauge theory dynamics

量子色动力学（QCD）是我们关于原子核相互作用的理论。我们在QCD中进行预测的标准理论工具，微动理论，在试图研究超高温系统的动力学时失败了，比如早期宇宙中存在的东西，以及我们现在可以在实验室中通过高能重离子碰撞创造的东西。我将研究改进摄动理论的理论预测方法。一种攻击途径将是改进微扰理论的方法，称为“恢复”。具体来说，我将研究非abel规范理论（如QCD）的3环、3粒子不可约还原。作为热身，我将首先在三维空间中研究理论，在三维空间中可以对resume方法进行系统的测试；如果可行，我将尝试将其应用于物理3空间+ 1时间维度。此外，我将研究另一种方法的系统学，它完全避免了对摄动理论的需要——相对论流体动力学。流体动力学研究表明，由重离子碰撞产生的夸克-胶子等离子体是已知的“最完美的”流体，在适当的单位测量时具有最低的粘度。我想帮助量化它，弄清楚水动力处理到底有多自洽和可靠。

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.