RUI: Topics in Planar Physics

本计画包含（2+1）维理论中两个不同主题的研究。 这些低维模型的易处理性增加，允许在高维理论中无法完成的显式计算。 1）规范场的非微扰方面PI及其合作者为规范场发展了一种特殊的矩阵参数化，以发展（2+1）维Yang-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高阶修正的计算弦张力，研究屏蔽与禁闭在这个框架下，并包括夸克自由度。2）非对易理论和量子霍尔效应（QHE）最近出现了一个有趣的联系QHE和非对易场论。 PI和合作者以前的研究表明，Polychronakos提出的（非交换）有限矩阵模型描述有限范围的分数量子霍尔流体（对于1/m的填充分数）在小距离处与标准波函数不一致，并对矩阵模型方法提出质疑。 矩阵模型和标准方法之间的对应关系将被探索和扩展，以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.