RUI: Topics in Planar Physics

Research Foundation Of The City University Of New York (Lehman), Bronx NY

Investigators

Abstract

This project involves research on two different topics in (2+1)-dimensional theories. Increased tractability of these lower dimensional models allows explicit calculations that cannot be done in higher dimensional theories. These calculations yield important insights that may also be relevant for higher dimensional theories. 1) Nonperturbative aspects of gauge theories. The PI and collaborators have developed a special matrix parametrization for the gauge fields in order to develop a gauge invariant Hamiltonian analysis of Yang-Mills theory in (2+1) dimensions. Recent results will be extended to analyze higher order corrections to the calculated string tension, investigate screening versus confinement in this framework, and include quark degrees of freedom. 2) Noncommutative theories and quantum Hall effect (QHE). There has recently appeared an interesting connection between QHE and noncommutative field theory. Previous studies by the PI and collaborator indicate that a (noncommutative) finite matrix model proposed by Polychronakos to describe fractional quantum Hall fluids of finite extent (for a filling fracton of 1/m) does not agree at small distances with standard wavefunctions and calls into question the matrix model approach. The correspondence between the matrix model and standard approaches will be explored and extended to include more general filling factors and electron degrees of freedom.