Massive Schwinger model within mass perturbation theory

TL;DR

This paper provides a comprehensive analysis of the massive Schwinger model using mass perturbation theory, including vacuum energy, bound states, and scattering processes, extending understanding beyond the massless case.

Contribution

It introduces detailed mass perturbation techniques for the massive Schwinger model, deriving Feynman rules, and analyzing bound states and scattering phenomena.

Findings

Computed vacuum energy density and related quantities.

Identified stable and unstable bound states with their masses and decay widths.

Analyzed scattering processes with resonances and particle production thresholds.

Abstract

In this article we give a detailed discussion of the mass perturbation theory of the massive Schwinger model. After discussing some general features and briefly reviewing the exact solution of the massless case, we compute the vacuum energy density of the massive model and some related quantities. We derive the Feynman rules of mass perturbation theory and discuss the exact $n$-point functions with the help of the Dyson-Schwinger equations. Further we identify the stable and unstable bound states of the theory and compute some bound-state masses and decay widths. Finally we discuss scattering processes, where the resonances and particle production thresholds of the model are properly taken into account by our methods.