Constructive Quantum Field Theory

Suny At Buffalo, Amherst NY

Investigators

Abstract

0070905 Dimock The goal of this project is to study quantum field theory models with full mathematical rigor. This is useful to clarify the structure of quantum field theory, and to enhance its predictive power. Quantum field theory is primarily a theory of elementary particle physics, but it also has an important role to play in classical statistical mechanics. Specific goals are as follows. (1.) A construction of quantum electrodynamics on a three dimensional torus. This is a step toward control of quantum electrodynamics and/or quantum chromodynamics in four dimensions, both of central importance in physics. (2.) The construction of a non-Gaussian fixed point for the renormalization group for an N-component scalar field in three dimensions. This would be progress toward understanding a wide range of critical phenomena. (3.) A study of the Higgs mechanism for non-Abelian gauge fields on a lattice. The Higgs mechanism is an important feature of theories of the weak interactions.