Overview on the anomaly and Schwinger term in two-dimensionalQED

Abstract

In the literature there exist many articles dealing with different treatments of the axial anomaly. We wanted to review some of those treatments using as a very simple example two-dimensional QED and to show how these different treatments are connected to each other. We showed how the anomaly arises because of the behaviour of some n-point functions in different treatments (perturbative, dispersive, in BJL limit) and how this behaviour can be traced to the very definition of the Dirac vacuum. Another feature of two-dimensional QED is the solvability of the massless case (Schwinger model). This we could use to demonstrate some methods of exactly solving it and to relate the exact solution to the previous results of the article. So the aim of the article is on the one hand to give an overview on twodimensional Supported by «Fonds zur Forderung der wissenschaftlichen Forschung in Osterreich», Projekt No. P8444-TEC.