Constructive Quantum Field Theory

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The purpose of the project is to construct and study mathematically precise quantum field theory models. The broader goal is sharpen our understanding of quantum field theory and increase its predictive power, thereby deepening our understanding of elementary particle physics and critical phenomena in statistical mechanics. The project particularly emphasizes the renormalization group. This is a widely applicable method for analyzing asymptotic behavior in space or time, and another broad goal is to make renormalization group techniques more precise, systematic, and easy to use. Specific project goals are: (1.) the construction of non-Gaussian fixed points for the renormalization group, and a study of the associated anomalous critical exponents, (2.) the construction of quantum electrodynamics and/or non-Abelian gauge theories in three space-time dimensions, and (3.) the study of mass generation in a scalar model simulating non-Abelian gauge theories.