Constructive Quantum Field Theory

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0070905DimockThe goal of this project is to study quantum field theory modelswith full mathematical rigor. This is useful to clarify thestructure of quantum field theory, and to enhance itspredictive power. Quantum field theory is primarily a theoryof elementary particle physics, but it also has an importantrole to play in classical statistical mechanics. Specific goalsare as follows.(1.) A construction of quantum electrodynamicson a three dimensional torus. This is a step toward controlof quantum electrodynamics and/or quantum chromodynamics infour dimensions, both of central importance in physics.(2.) The construction of a non-Gaussian fixed point for therenormalization group for an N-component scalar field in threedimensions. This would be progress toward understanding a widerange of critical phenomena.(3.) A study of the Higgs mechanism for non-Abelian gauge fieldson a lattice. The Higgs mechanism is an important feature oftheories of the weak interactions.