Functional methods

Abstract

Our derivation of exact FRG equations in Chap. 7 will be based on the concept of generating functionals of several types of Green functions and vertex functions. For a self-contained introduction to the FRG it is therefore necessary to properly define the various generating functionals and develop some intuition for the meaning of the associated correlation functions, which we shall do in this chapter. Moreover, we shall use the invariance properties of generating functionals under shift and symmetry transformations to derive so-called Dyson-Schwinger equations of motion and Ward identities relating different types of correlation functions. Of course, comprehensive introductions to functional methods can be found in several excellent textbooks (Negele and Orland 1988, Zinn-Justin 2002, Rammer 2007). In this context we also mention the more specialized books by Vasiliev (1998) and by Fried (1972, 2002), which emphasize the formulation of field theory in terms of functional derivatives. © 2010 Springer-Verlag Berlin Heidelberg.