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.
