RUI: Studies on gauge theories and quantum Hall fluids

对规范理论的非微扰方面的理解，如禁闭和质量间隙，是理论物理中两个突出的问题。PI及其合作者已经为（2+1）维的Yang-Mills理论开发了一种哈密顿方法。PI建议进一步研究对计算的弦张力的高阶修正以及对Casimir标度规则的相应影响。她希望改进该理论的胶球谱的初步分析结果，并将这些想法应用于研究有限温度下的解除禁闭。PI将研究的另一个项目是更高维度的量子霍尔效应（QHE）。希望本研究能提供一个丰富的框架，研究新的想法模糊空间，非交换场论，矩阵模型和玻色化在更高的维度。该项目的完成预计将大大有助于我们对规范理论的非微扰方面的理解; QHE，模糊空间，非对易场论，矩阵模型和更高维度的玻色子化之间的新兴联系开辟了不同领域之间的新的跨学科路径，如量子场论，弦理论，凝聚态物理和数学物理。纽约市立大学莱曼学院是一所以本科为主的机构，有大量的女性（72%）和少数民族（78%）学生。PI充当学生的榜样，并积极参与课程开发。她开发了一门关于声音物理学的课程，吸引了学院许多音乐专业和演讲专业的学生。

The understanding of the non-perturbative aspects of gauge theories, such as confinement and the mass gap, are two outstanding problems in theoretical physics. The PI and collaborators have developed a Hamiltonian approach for Yang-Mills theories in (2+1) dimensions The PI proposes to further study higher order corrections to the calculated string tension and the corresponding effect on the Casimir scaling rule. She hopes to improve preliminary analytic results on the glueball spectrum of the theory, and apply these ideas to study deconfinement at finite temperatures. Another project that the PI will investigate is the Quantum Hall effect (QHE) in higher dimensions. It is hoped that this research will provide a rich framework for studying new ideas on fuzzy spaces, noncommutative field theories, matrix models and bosonization in higher dimensions. The completion of this project is expected to contribute considerably to our understanding of the nonperturbative aspects of gauge theories; the emerging connections between QHE, fuzzy spaces, noncommutative field theories, matrix models and bosonization in higher dimensions open up new interdisciplinarypaths between different areas such as quantum field theory, string theory, condensed matter physics and mathematical physics. Lehman College, CUNY, is a predominantly undergraduate institution with a large number of female (72%) and minority (78%) students. The PI acts as a role model for the students and is very involved in curriculum development. She has developed a course on the Physics of Sound which has attracted many Music Majors at the College as well as Speech Majors.