Constructive Quantum Field Theory

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This project has as a goal the mathematically rigorous construction and study of quantum field theory models. This would be an aid to the understanding of elementary particle physics, ultimately predicting particle masses, scattering amplitudes, and so forth. It would also help in the study of some properties of many body systems, particularly critical phenomena. Specific models to be studied are the following. (1.) The Sine- Gordon model in 2 dimensions. This is a scalar field with a periodic interaction. It also describes a classical Coulomb gas. (2.) phi-fourth models in 3 and 4 dimensions. These are scalar fields with a quartic self-interaction. (3.) Quantum electrodynamics in 3 dimensions. This is the theory of electrons and photons. (4.) Yang Mills in 3 and 4 dimensions. This is a pure non- Abelian gauge theory.