Some non-perturbative results in relativistic field theory

This thesis contains the descriptions of two new non-perturbative results in relativistic field theory. The first part of the thesis describes a transformation which can be used to relate the strong coupling limit of the (theta 4)3 quantum field theory to the weak coupling limit of the same theory. This transformation can be used to show the existence of a phase transition in the above theory as the coupling constant is increased with the mass parameter held fixed. The derivation of the transformation involves Zimmerman normal operator techniques. The second part of the thesis describes a variational calculation of the classical interactions of 't Hooft monopoles. These interactions are interesting because 't Hooft monopoles appear as instantons in the Georgi-Glashow theory of weak and electromagnetic interactions. The interactions of the instantons are directly related to the question of confinement of the fermions in this theory.U of I OnlyThesi