Renormalization Group Methods

Abstract

This chapter begins with a brief introduction to path integral methods, since the path integral formulation of quantum field theory is a natural home for examining the generality of renormalization group (RG) methods. In particle physics and condensed matter physics, the main set of tools for determining how physical processes at longer scales depend on short-distance physics are RG methods. The RG was widely viewed as having put the earlier renormalization methods on secure physical foundations. The path integral representation of a quantum field theory (QFT) provides a particularly natural home for RG methods. RG methods will form a significant portion of any modern introduction to QFT. RG methods have also been put to considerable philosophical use, most notably in debates concerning emergence and reduction. The chapter concludes by considering the benefits that thinking in terms of theory space has for the task of defining and classifying QFTs.