Introduction to Chiral Perturbation Theory

Abstract

This article provides a pedagogical introduction to the basic concepts of chiral perturbation theory and is designed as a text for a two-semester course on that topic. Section 1 serves as a general introduction to the empirical and theoretical foundations which led to the development of chiral perturbation theory. Section 2 deals with QCD and its global symmetries in the chiral limit; the concept of Green functions and Ward identities reflecting the underlying chiral symmetry is elaborated. In Section 3 the idea of a spontaneous breakdown of a global symmetry is discussed and its consequences in terms of the Goldstone theorem are demonstrated. Section 4 deals with mesonic chiral perturbation theory and the principles entering the construction of the chiral Lagrangian are outlined. Various examples with increasing chiral orders and complexity are given. Finally, in Sect. 5 the methods are extended to include the interaction between Goldstone bosons and baryons in the single-baryon sector, with the main emphasis put on the heavy-baryon formulation. At the end, the method of infrared regularization in the relativistic framework is discussed.