RUI: Topics in Planar Physics

这个项目涉及对(2+1)维理论中两个不同主题的研究。这些低维模型的可处理性增加，允许进行在高维理论中无法完成的显式计算。这些计算产生了重要的见解，可能也与高维理论有关。1)规范理论的非微扰方面。PI和合作者开发了一种特殊的规范场矩阵参数化，以便在(2+1)维中发展杨-Mills理论的规范不变哈密顿分析。最近的结果将被扩展到分析计算的弦张力的高阶修正，在这个框架中研究屏蔽与限制，并包括夸克的自由度。2)非对易理论和量子霍尔效应(QHE)。最近在QHE和非对易场论之间出现了有趣的联系。PI和合作者以前的研究表明，Polychronakos提出的描述有限范围(填充分数为1/m)分数量子霍尔流体的(非对易)有限矩阵模型在小距离上与标准波函数不一致，并对矩阵模型方法提出了质疑。将探索矩阵模型和标准方法之间的对应关系，并将其扩展到包括更一般的填充因子和电子自由度。

This project involves research on two different topics in (2+1)-dimensional theories. Increased tractability of these lower dimensional models allows explicit calculations that cannot be done in higher dimensional theories. These calculations yield important insights that may also be relevant for higher dimensional theories.1) Nonperturbative aspects of gauge theories.The PI and collaborators have developed a special matrix parametrization for the gauge fields in order to develop a gauge invariant Hamiltonian analysis of Yang-Mills theory in (2+1) dimensions. Recent results will be extended to analyze higher order corrections to the calculated string tension, investigate screening versus confinement in this framework, and include quark degrees of freedom.2) Noncommutative theories and quantum Hall effect (QHE).There has recently appeared an interesting connection between QHE and noncommutative field theory. Previous studies by the PI and collaborator indicate that a (noncommutative) finite matrix model proposed by Polychronakos to describe fractional quantum Hall fluids of finite extent (for a filling fracton of 1/m) does not agree at small distances with standard wavefunctions and calls into question the matrix model approach. The correspondence between the matrix model and standard approaches will be explored and extended to include more general filling factors and electron degrees of freedom.