The structure of renormalization theory: renormalization, form factors and resummations in scalar field theory

This paper describes a recent approach to renormalization theory leading to a description of the renormalized series for the effective potential and for the Schwinger functions in terms of a family of `form factors' containing an important resummation of `infinitely many ordinary Feynman diagrams'. The ideas exposed in the paper overlap partially with those of J. Polchinski and were developed by the author and F. Nicolo`, extending previous partial results and techniques of these authors and their collaborators.