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 interdisciplinary paths 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.
The findings of this project are concentrated in two main areas: nonperturbative aspects of Quantum Chromodynamics (QCD) and the Casimir effect. The analytical understanding of nuclear forces, as described by the theory of QCD, and especially nonperturbative phenomena such as the binding of quarks and gluons to form nuclei, remains one of the outstanding problems in theoretical physics. The PI and collaborators continued their work on the Hamiltonian approach they have developed in studying such phenomena in a simpler, lower dimensional, yet physically relevant setting. Previously obtained results on the binding forces for quarks were extended by a more detailed calculation. Casimir effect refers to the phenomenon where quantum fluctuations of fields produce a measurable effect, a macroscopic force between conducting plates in vacuum. These forces, although small, can now be experimentally measured with good accuracy and they play an important role in the design of nano-scale mechanical devices. The PI and collaborators developed a new analytical approach, well suited to studying diffractive corrections to the Casimir effect in geometries with edges and apertures at zero and finite temperatures. Various geometries with edges and apertures were studied; our analytical results agree very well with previous numerical studies. These project outcomes resulted from a collaboration between the high energy groups at Lehman and City College, CUNY. This research project has contributed towards the training of a postdoctoral research associate who was partially involved in the collaboration and has played an important role in fostering an active research environment at Lehman College, CUNY, a predominantly undergraduate institution with a large number of minority students.
