RUI: Studies in Field Theory: Casimir Effect, Yang-Mills Theory

该奖项为Dimitra Karabali教授在纽约Lehman学院校园开展的RUI研究项目提供资金。 该项目涉及两个主题。第一个重点是卡西米尔效应，一种真空中的中性物体由于场的量子涨落而经历宏观力的现象。这些力量，虽然可以忽略不计，在大的距离，成为主导地位，并发挥重要作用，在距离尺度相关的纳米尺度的机械设备的设计。准确的实验观测这一现象激发了新的理论方法在处理不同的几何形状，温度等的影响，作为她的研究的一部分，教授Karabali将继续她的卡西米尔力的研究，特别是从衍射的贡献，由于边界边缘在各种设置。第二个主题侧重于量子色动力学中的非微扰现象的理解，该理论描述了夸克和胶子之间的相互作用，原子核的基本组成部分。她将继续她的工作，建立在以前介绍的技术范围内的量子波动方程对理解限制。 预计该项目将产生广泛的影响。具体而言，它将在培养一个积极的，以科学为导向的研究环境中发挥重要作用，在雷曼学院，纽约市立大学，一个主要的本科院校与大量的少数民族学生，被指定为西班牙裔服务机构由美国教育部。该项目还将支持雷曼和纽约市立大学城市学院高能理论研究小组之间的合作，研究Casimir效应中的衍射贡献和（2+1）Yang-Mills理论中的非微扰现象。 Casimir效应的精确实验观测激发了新的理论方法，在处理不同的几何形状，温度等的影响，PI和合作者已经开发出一种新的方法，非常适合于研究由于边界边缘和孔径不同的几何形状，有限的温度和一般的边界条件的衍射修正Casimir能量。该项目将扩展该方法的方向：计算更高的点函数重要的内场成像和传输;列入领域与自旋可能的应用领域的频谱几何;依赖于曲率（包括外在和内在），自旋和几何形状的导电板上的孔之间的相互作用能。对杨-米尔斯理论中的禁闭、质量隙等非微扰现象的理解是理论物理中的一个突出问题。在一系列的论文中，PI和合作者已经为（2+1）维的Yang-Mills理论开发了一种哈密顿方法，已经产生了许多有趣的结果，与晶格计算非常一致。最近的真空波函数中得到的哈密顿形式主义已被用来推导出一个有效的行动，这是协变的，使某些问题更容易分析。本项目将探索这种有效作用量的性质，特别是在这种作用量的一个扇区中存在的Z_N涡旋的作用，以理解不同表示的屏蔽与限制，以及该理论的激发态谱和对胶球质量的影响。

This award provides funding for an RUI research project carried out by Professor Dimitra Karabali at the Lehman College campus of the City University of New York (CUNY). The project addresses two topics. The first focuses on the Casimir effect, a phenomenon where neutral objects in vacuum experience macroscopic forces due to the quantum fluctuations of fields. These forces, although negligible at large distances, become dominant and play an important role at distance scales relevant in the design of nano-scale mechanical devices. Accurate experimental observations of this phenomenon have motivated new theoretical approaches in dealing with the effects of different geometries, temperature, etc. As part of her research, Professor Karabali will continue her studies of the Casimir forces and in particular contributions from diffraction due to boundary edges in a variety of settings. The second topic focuses on the understanding of nonperturbative phenomena in quantum Chromodynamics, the theory describing the interactions between quarks and gluons, the fundamental constituents of atomic nuclei. She will continue her work by building on previously introduced techniques within the context of quantum wave equations towards understanding confinement. This project is expected to have significant broader impacts. Specifically, it will play an important role in fostering an active, scientifically oriented research environment at Lehman College, CUNY, a predominantly undergraduate institution with a large number of minority students, designated as a Hispanic serving institution by the U.S. Department of Education. It will also support collaboration between the high-energy theory research groups at Lehman and at City College, CUNY.The project addresses diffractive contributions in Casimir effect and nonperturbative phenomena in (2+1) Yang-Mills theory. Accurate experimental observations of the Casimir effect have motivated new theoretical approaches in dealing with the effects of different geometries, temperature etc. The PI and collaborators have developed a novel approach well-suited to studying diffractive corrections to Casimir energy due to boundary edges and apertures for different geometries, finite temperature and general boundary conditions. This project will extend this method towards: the calculation of higher-point functions important inner field imaging and transmission; the inclusion of fields with spin with possible applications to the field of spectral geometry; the dependence of the interaction energy between holes on conducting plates on curvature (both extrinsic and intrinsic), spin and geometry. The understanding of nonperturbative phenomena in Yang-Mills theories, such as confinement and mass gap, is one of the outstanding problems in theoretical physics. In a series of papers, the PI and collaborators have developed a Hamiltonian approach for Yang-Mills theories in (2+1) dimensions, which has already produced a number of interesting results, in good agreement with lattice calculations. Recently the vacuum wave function obtained in the Hamiltonian formalism has been used to derive an effective action, which, being covariant, renders certain questions more amenable to analysis. This project will explore the properties of this effective action and in particular the role of the Z_N vortices, present in a sector of this action, in understanding screening versus confinement for different representations as well as the spectrum of the excited states of the theory and implications on glueball masses.