RUI: Topics in Planar Physics

本项目涉及（2+1）维理论中两个不同主题的研究。这些较低维度模型的可追溯性增加，使得在高维理论中无法进行的显式计算成为可能。这些计算产生了重要的见解，可能也与高维理论有关。1)规范理论的非摄动方面。为了在（2+1）维中发展Yang-Mills理论的规范不变哈密顿分析，PI和合作者已经为规范场开发了一种特殊的矩阵参数化。最近的结果将扩展到分析计算弦张力的高阶修正，研究该框架下的屏蔽与限制，并包括夸克自由度。2)非交换理论与量子霍尔效应。QHE和非交换场论之间最近出现了一种有趣的联系。PI和合作者先前的研究表明，Polychronakos提出的（非交换的）有限矩阵模型用于描述有限范围的分数量子霍尔流体（对于1/m的填充分数）在小距离上与标准波函数不一致，并且对矩阵模型方法提出了质疑。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.