Progress report for a research program in theoretical high-energy physics

This year's research has dealt with a wide range of topics in High-Energy Theoretical Physics. New results have been found in: the formulation and renormalization of contracted Lie groups, as applied to symmetry breaking in field theory; the application of some quantum field theory techniques to fluid turbulence; the application of a strong-coupling method to continuum QED; renormalization properties of the super-symmetric Liouville action and a study of Pomeron properties in the context of this action; a two-dimensional XY-model in a quenched, random field; computer-oriented studies of finite-element methods in quantum field theory; an explanation of multiple generations in terms of composite fermions and Higgs scalars; and computer-simulation methods in loop space. The large-N limit in quantum field theory received much concentrated attention, with studies approaching this question from the point of view of the collective field method using Wilson loops, the large-N limit in symplectic models and in two-dimensional field theory, and the so-called reduced lattice models, with and without spontaneous symmetry breaking. A numerical, computer simulation method for solving the large N limit was developed. Another subject in which much effort has been expended at Brown is that of Monte-Carlo techniques for QCD, dealing specifically with questions of fermion masses, chiral symmetry breaking and confinement. A vast amount of work has been accomplished in understanding the deep structure of Grand Unification Theories