Field-theoretical renormalization group

Abstract

The concept of the RG was originally introduced in the context of quantum field theory by Stueckelberg and Petermann (1953) and by Gell-Mann and Low (1954), long before Wilson's seminal works. Although the field-theoretical RG is less general than the Wilsonian RG and can only be applied to so-called renormalizable theories (we shall explain in this chapter what this means), calculations beyond the leading order in the number of loop integrations are usually simpler within the field theoretical RG if it is applicable. Here, we shall briefly introduce the main ideas of the field-theoretical RG method. 1 More detailed introductions can be found in the authoritative book by Zinn-Justin (2002) or in many other textbooks on quantum field theory such as (Sterman 1993, Peskin and Schroeder 1995, Zee 2003). © 2010 Springer-Verlag Berlin Heidelberg.