GAUGE THEORIES AT ZERO AND NONZERO TEMPERATURES

量子色动力学（Quantum Chromodynamics，简称QCD）是目前公认的、经过充分验证的理论，它总结了迄今为止我们对夸克（核物质的基本组成部分）和胶子（负责核力的粒子）的知识。在布鲁克海文的相对论重离子对撞机（RHIC）上，重原子核的碰撞有望产生一种新的物质状态，即所谓的夸克-胶子等离子体，它将为QCD提供一个重要的新试验场，在各种物理参数（如压力和温度）的极端条件下，从而有可能导致理论的进一步阐明、确认或扩展。在这种条件下预期的粒子间力减弱，即所谓的筛选效应，将是解释RHIC数据的一个重要因素。本项目将对夸克-胶子等离子体中不同类型的筛选效应进行理论研究，以及一些相关问题。基本的数学策略，这是先前使用的技术的扩展，将QCD与较低和较高时空维度的合适理论联系起来，这是最近提供重要新见解的一种方法。在适当的情况下，所获得的结果将与这些理论的基于计算机的数值分析相关联。

Quantum Chromodynamics or QCD is the currently accepted and well-tested theory which sums up our knowledge, to date, of quarks, which are the fundamental constituents of nuclear matter, and of gluons, the particles responsible for nuclear forces. The collisions of heavy atomic nuclei at the relativistic heavy ion collider (RHIC) in Brookhaven is expected to produce a new state of matter, the so-called quark-gluon plasma, which will provide an important new testing ground for QCD, with extreme conditions for various physical parameters such as pressure and temperature, and thus potentially leading to further elucidation,confirmation or extension of the theory. The expected weakening of interparticle forces under such conditions, the so-called screening effects, will be an important ingredient in the interpretation of data from RHIC.In this project, theoretical investigations of different types of screening effects in the quark-gluon plasma, as well as a number of related questions, will be carried out. The basic mathematical strategy, which is an extension of previously used techniques, will be to relate QCD to suitable theories in lower and higher number of spacetime dimensions, an approach which has provided significant new insights recently. Whereverappropriate, results obtained will be correlated with numerical computer-based analysis of such theories.