Gauge theories in (2+1) dimensions and quantum Hall effect in higher dimensions

在过去的几年里，PI和合作者已经在两个空间维度上发展了杨-米尔理论的规范不变哈密顿分析。得到了规范不变位形空间上积分测度的精确表达式、真空波的表达式和弦张力的解析公式等几个有趣的结果。由于最近对该主题的重新关注，PI提出分析计算弦张力的高阶修正，研究在该框架下伴随物质与约束的筛选，并应用该哈密顿公式研究（2+1）维无质量费米子QED中的动态质量生成问题。

Over the last few years the PI and collaborators, have developed a gauge invariant Hamiltonian analysis of Yang-Mill theory in two spatial dimensions. Several interesting results were derived such as an exact expression for the integration measure on the gauge invariant configuration space, an expression for the vacuum wave and an analytic formula for the string tension. Motivated by recent renewed interest in this topic, the PI proposes to analyze higher order corrections to the calculated string tension, investigate screening of adjoint matter versus confinement in this frame work and apply this Hamiltonian formulation to study issues of dynamical mass generation in (2+1) dimensional QED with massless fermions.