RUI: Nonperturbative Analyses in Field Theory

该奖项为纽约莱曼学院的Dimitra Karabali教授的研究活动提供资金。高能物理学的重点是物质的基本组成部分及其相互作用。 作为她的研究的一部分，Karabali教授的目标是促进我们对描述这些相互作用的基础理论的理解，特别是量子色动力学（QCD），该理论描述了构成所有原子核的夸克和胶子之间的作用力。 虽然QCD在解释大量实验数据方面非常成功，但这些力产生的某些效应至关重要，但人们对它们的了解却很少。 这些包括夸克结合在一起的机制，产生大质量的复合物体。 作为这个项目的一部分，PI将继续她的工作，开发技术，可以导致更好地了解这些影响。 该项目还旨在探索与凝聚态物理学中基本问题的联系，例如量子霍尔效应（QHE）。 著名的QHE与强磁场存在下的电子系统有关，多年来，它提供了一个框架，可以研究许多重要理论思想的相互作用，这些理论思想对于最终统一引力与其他基本自然力至关重要。 因此，拟议的研究将通过提高我们对基础科学的认识来促进国家利益。 预计该项目还将产生更广泛的重大影响。它将发挥重要作用，在培养一个积极的，以科学为导向的研究环境在雷曼学院，纽约市立大学，主要是本科生，少数民族服务的机构，并在吸引学生物理和本科研究。该项目还将提供研究生培训，并促进雷曼兄弟和纽约市立大学城市学院研究人员之间的合作。用更技术性的术语来说，本提案的主要目标可分为两个专题。 第一个是卡西米尔效应和杨-米尔斯理论。 本文将在二维Yang-Mills理论的Hamilton方法框架内扩展Casimir能量的研究，作为研究该理论非微扰特性的另一个探索。第二个是弯曲空间上的量子霍尔效应和对产生。 该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award funds the research activities of Professor Dimitra Karabali at Lehman College of the City University of New York. High-energy physics focuses on the fundamental building blocks of matter and their interactions. As part of her research, Professor Karabali aims to advance our understanding of the underlying theories describing these interactions, in particular Quantum Chromodynamics (QCD), the theory describing the forces between the quarks and gluons making up all atomic nuclei. Although QCD has been very successful in explaining a host of experimental data, there are certain effects to which these forces give rise which are of central importance and yet poorly understood. These include the mechanism by which quarks are bound together, producing massive composite objects. As part of this project, the PI will continue her work developing techniques that can lead to a better understanding of these effects. This project also aims to explore connections with fundamental problems in condensed-matter physics, such as the quantum Hall effect (QHE). The celebrated QHE, which is associated with systems of electrons in the presence of a strong magnetic field, has, over the years, provided a framework in which to study the interplay of many important theoretical ideas which are critical for eventually unifying gravity with the other fundamental forces of nature. As a result, the proposed research will advance the national interest by improving our knowledge of fundamental science. This project is also expected to have significant broader impacts. It will play an important role in fostering an active, scientifically oriented research environment at Lehman College, CUNY, a predominantly undergraduate, minority-serving institution, and in attracting students to physics and to undergraduate research. The project will also provide graduate-student training and foster collaboration between researchers at Lehman and City Colleges, CUNY. In more technical terms, the key objectives of this proposal can be organized in two topics. The first is the Casimir effect and Yang-Mills theory. Here it will extend the study of Casimir energy within the framework of the Hamiltonian approach for Yang-Mills theories in two spatial dimensions, as another probe to study the nonperturbative features of the theory. The second is the quantum Hall effect on curved spaces and pair production. Here it will use the quantum Hall effect on curved spaces as a tool to study the effect of curvature on pair creation and vacuum instability.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.