9507829 Alvarez Quantum field theory is the primary tool for studying elementary particle theory. It has several unresolved problems, a key one being the relationship between fermions and bosons (supersymmetry). It is believed that there are other symmetries which have not yet been discovered and that new mathematical techniques will need to be found to analyze them. This research seeks to address these problems in part directly and in part through knowledge acquired in the study of statistical mechanics systems and of string theory. ***
