ar X iv : h ep - p h / 05 05 26 5 v 1 3 1 M ay 2 00 5 A Chiral Perturbation Theory

The course was addressed to PhD students with both rather different interests and background in experimental and theoretical nuclear and particle physics. The students were assumed to be familiar with elementary concepts of field theory and relativistic quantum mechanics. The goal of the course was to provide a pedagogical introduction to the basic concepts of chiral perturbation theory (ChPT) in the mesonic and baryonic sectors. We have tried to also work out those pieces which by the " experts " are considered as well known. In particular, we have often included intermediate steps in derivations in order to facilitate the understanding of the origin of the final results. We have tried to keep a reasonable balance between mathematical rigor and illustrations by means of simple examples. Some of the topics not directly related to ChPT were covered in extra lectures in the afternoon. By preparing numerous exercises, covering a wide range of difficulty—from very easy to quite difficult—, we hoped to take the different individual levels of experience into account. Ideally, at the end of the course, a participant (or a reader of these notes) should be able to perform simple calculations in the framework of ChPT and to read the current literature. These lecture notes include the following topics. Chapter 1 deals with QCD and its global symmetries in the chiral limit, explicit symmetry breaking in terms of the quark masses, and the concept of Green functions and Ward identities reflecting the underlying chiral symmetry. In Chapter 2 the idea of a spontaneous breakdown of a global symmetry is discussed and its consequences in terms of the Goldstone theorem are demonstrated. Chapter 3 deals with mesonic chiral perturbation theory and the principles entering the construction of the chiral Lagrangian are outlined. In Chapter 4 the methods are extended to include the interaction between Goldstone bosons and baryons in the single-baryon sector. Sections marked with an asterisk may be omitted in a first reading. Readers interested in the present status of applications are referred to Acknowledgements The authors would like to thank the coordinator Matthias F. M. Lutz and the co-organizers Michael Birse and W. Vogelsang for the invitation to participate in the program. Moreover, we would like to thank Prof. for the hospitality and the pleasant working conditions at ECT *. M. R. S. acknowledges the support through a Marie Curie fellowship. S. S. would like to thank the …