40 - Introduction

Summary

In the previous parts of this book, we have studied different methods based on power corrections, namely renormalons, instantons and the SVZ-expansion in terms of condensates and eventual quadratic corrections, which are one important aspect of non-perturbative QCD. In this part, we shall shortly discuss the other most popular non-perturbative methods used in QCD for studying the low-energy properties of the hadrons and of QCD. These are:

• Lattice gauge theory

• Chiral perturbation theory (ChPT)

• Models of the QCD effective action

• Heavy quark effective theory (HQET)

• Potential approaches for quarkonia.

The method and phenomenology of QCD Spectral Sum Rules (QSSR) which will be discussed in more details will be devoted to a new part. Here, we do not aim to present a complete review and references but we shall limit ourselves to the outline of the general features of the different approaches. A more extensive list of non-perturbative methods, which will not be discussed here, such as the:

• Skyrme model

• Bag models

• Discretized light-cone quantization

can be found in [3]. We shall shortly discuss in the chapter dedicated to the heavy quarks, the two approaches:

• Potential and quark models

• Stochastic vacuum model

• Non-relativistic effective theories

which are discussed in details in some other reviews (see e.g. [51]).We shall complete this part by a short discussion on monopole and confinement.