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Yang-Mills theory at finite temperatures

有限温度下的杨-米尔斯理论

基本信息

批准号：
222131839
负责人：
Professor Dr. Hugo Reinhardt
金额：
--
依托单位：
Institut für Theoretische Physik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2013
资助国家：
德国
起止时间：
2012-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/222131839?language=en
关键词：
Yang Mills theory finite temperatures

项目摘要

The goal of the proposed research project is a detailed understanding of the phase diagram of QCD, in particular in the regime of finite baryon density which is currently unaccessible to lattice simulations. For this purpose the variational approaches to continuum quantum field theory at finite temperatures which were developed in the first funding period are supposed to be extended to full QCD at finite chemical potential. These variational approaches are based on either the Hamiltonian formulation of QCD in Coulomb gauge, or the covariant path integral approach in Landau gauge. In this context, it is planned to first study the relevant propagators at finite temperature and chemical potential, from which the order parameters for confinement (Polyakov loop) and chiral symmetry breaking (quark condensate), as well as the dual quark condensate will be computed. Furthermore, it is planned to study QCD at finite temperature and chemical potential in the presence of an external homogeneous magnetic field using the covariant variational approach. To this end, the technique of (approximate) partial summation of Landau levels developed in the first funding period shall be used to compute the quark condensate as a function of the magnetic field strength in the regime most relevant for relativistic heavy ion reactions. In addition to these continuum approaches, the quark propagators and vertices of relevance for the Hamiltonian approach in Coulomb gauge shall be studied by means of lattice simulations.

拟议的研究项目的目标是详细了解QCD的相图，特别是在有限重子密度的制度，这是目前无法访问的晶格模拟。为此，在第一个资助期内发展起来的有限温度下连续量子场论的变分方法应该推广到有限化学势下的全QCD。这些变分方法要么基于库仑规范下的量子色动力学的哈密顿公式，要么基于朗道规范下的协变路径积分方法。在这种情况下，计划首先研究有限温度和化学势下的相关传播子，从中计算禁闭（Polyakov环）和手征对称性破缺（夸克凝聚）以及双夸克凝聚的序参数。此外，我们还计划利用协变分方法研究在有限温度和化学势下，外加均匀磁场下的QCD。为此，应使用第一个供资期开发的朗道能级部分求和（近似）技术，计算夸克凝聚体，作为与相对论重离子反应最相关的区域内磁场强度的函数。除了这些连续统方法外，我们还将通过格点模拟研究库仑规范中与哈密顿方法相关的夸克传播子和顶点。