On the U(1)-Problem of QED_2

TL;DR

This paper investigates the U(1)-problem in two-dimensional quantum electrodynamics (QED_2) with mass and flavor, using path integrals and bosonization to draw parallels with QCD and explore the theta-vacuum and related phenomena.

Contribution

It constructs a detailed bosonized model of QED_2 with mass and flavor, providing new insights into the U(1)-problem and theta-vacuum structures relevant to QCD.

Findings

Decomposition of the vacuum functional into clustering states.

Mapping of the model onto a generalized Sine-Gordon theory.

Insights into the theta-vacuum and U(1)-problem analogous to QCD.

Abstract

QED_2 with mass and flavor has in common many features with QCD, and thus is an interesting toy model relevant for four dimensional physics. The model is constructed using Euclidean path integrals and mass perturbation series. The vacuum functional is carefully decomposed into clustering states being the analogue of the theta-vacuum of QCD. Finally the clustering theory can be mapped onto a generalized Sine-Gordon model. Having at hand this bosonized version, several lessons on the theta-vacuum, the U(1)-problem and Witten-Veneziano-type formulas will be drawn. This sheds light on the corresponding structures of QCD.