Confinement and the analytic structure of the one body propagator in Scalar QED

TL;DR

This paper analyzes the one body propagator in Scalar QED, comparing different calculation methods and revealing how confinement affects the analytic structure of the propagator, with the exact solution maintaining real mass poles.

Contribution

It introduces an exact analytical Feynman-Schwinger representation for the propagator and compares it with approximate methods, highlighting confinement effects.

Findings

Exact solution yields real mass poles for all couplings.

Approximate methods show complex poles beyond a critical coupling.

Model demonstrates confinement despite real mass poles in the exact case.

Abstract

We investigate the behavior of the one body propagator in SQED. The self energy is calculated using three different methods: i) the simple bubble summation, ii) the Dyson-Schwinger equation, and iii) the Feynman-Schwinger represantation. The Feynman-Schwinger representation allows an {\em exact} analytical result. It is shown that, while the exact result produces a real mass pole for all couplings, the bubble sum and the Dyson-Schwinger approach in rainbow approximation leads to complex mass poles beyond a certain critical coupling. The model exhibits confinement, yet the exact solution still has one body propagators with {\it real} mass poles.