GAUGE THEORIES AT ZERO AND NONZERO TEMPERATURES

量子色动力学（QCD）是目前公认的和经过充分检验的理论，它总结了我们迄今为止对夸克和胶子的知识，夸克是核物质的基本组成部分，胶子是负责核力的粒子。 在布鲁克海文的相对论重离子对撞机（RHIC）上进行的重原子核碰撞预计将产生一种新的物质状态，即所谓的夸克-胶子等离子体，这将为QCD提供一个重要的新的试验场，为各种物理参数（如压力和温度）提供极端条件，从而可能导致进一步阐明，确认或扩展理论。在这种条件下，粒子间力的预期减弱，即所谓的屏蔽效应，将是解释RHIC数据的一个重要组成部分。在这个项目中，将对夸克-胶子等离子体中不同类型的屏蔽效应以及一些相关问题进行理论研究。基本的数学策略，这是以前使用的技术的扩展，将QCD与合适的理论在较低和较高的时空维度，最近提供了重要的新见解的方法。 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.