RUI: Studies on gauge theories and quantum Hall fluids

RUI：规范理论和量子霍尔流体研究

• 批准号: 0758008
• 负责人: Dimitra Karabali
• 金额: $ 9万
• 依托单位: Research Foundation Of The City University Of New York (Lehman)
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-11-01 至 2011-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0758008&HistoricalAwards=false
• 关键词: RUI; Studies; gauge; theories; quantum

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.

对规范理论的非微扰方面的理解，如禁闭和质量间隙，是理论物理中的两个突出问题。PI和合作者发展了(2+1)维杨-米尔斯理论的哈密顿方法。PI建议进一步研究对计算的弦张力的高阶修正以及相应的对Casimir标度规则的影响。她希望改进该理论胶球光谱的初步分析结果，并将这些想法应用于研究有限温度下的去禁闭。PI将研究的另一个项目是更高维度的量子霍尔效应(QHE)。希望这项研究将为研究模糊空间、非对易场论、矩阵模型和高维玻色化等新思想提供一个丰富的框架。这个项目的完成将有助于我们理解规范理论的非微扰方面；QHE、模糊空间、非对易场论、矩阵模型和高维玻色化之间的新联系开辟了不同领域之间的新的跨学科途径，如量子场论、弦理论、凝聚态物理和数学物理。纽约州立大学雷曼学院是一所以本科生为主的院校，有大量女性(72%)和少数族裔(78%)学生。PI作为学生的榜样，非常参与课程开发。她开发了一门关于声音物理的课程，这门课程吸引了学院许多音乐专业的学生以及演讲专业的学生。