Some approaches to renormalization

Abstract

This thesis attempts to give a survey of some approaches to quantum field theory and quantum electrodynamics. The earliest formulation of these theories implicitly assumed that many operations which were valid in non relativistic quantum mechanics had the same validity in field theory. This lead to many difficulties in interpreting divergent, or ambiguous, results. Subsequent theories have treated the mathematical operations more carefully and it has been realized that more powerful mathematical tools are needed to treat field theories compactly and rigorously. Here emphasis is given to these later approaches and in particular much of the development is based on the asymptotic formulation of the theory of interacting fields.