Chiral symmetry and the U(1) problem

This review gives a detailed account of recent progress in the U(l) problem from the point of view of the anomalous Ward identities and the large Ne expansion. Two important ingredients that go into the formulation of the U(l) problem, chiral symmetry and the QCD anomaly, are extensively discussed. The basic concepts and techniques of chiral symmetry and chiral perturbation theory, as realized in the Gell-Mann-Oakes- Renner scheme, are reviewed. The physical meaning of the anomaly is clarified and its effects are consistently implemented through the anomalous Ward identities. These equations are extensively analysed in the chiral and/or large Nc limits. The $ periodicity puzzle, its solution and the required spectrum of topological charge are discussed in the framework of chiral perturbation theory. Other aspects of the U(l) problem, such as: the means by which the /|' obtains its large mass, the details of the required (modified) Kogut-Susskind mechanism, phenomenological applications, effective chiral Lagrangians incorporating effects of the anomaly and proofs of spontaneous chiral symmetry breaking are considered from the viewpoint of the large Nc and topological expansions.