Confinement of electrons in QED2+1 and quarks in QCD3+1 in Temporal Euclidean space

TL;DR

This paper solves the ladder QED2+1 and QCD3+1 models directly in Minkowski and Temporal Euclidean spaces, demonstrating that solutions are equivalent in QED2+1 and showing confinement through complex fermion propagators.

Contribution

It provides a direct Minkowski space solution for ladder QED2+1 and extends the analysis to QCD3+1 in Temporal Euclidean space, highlighting confinement features.

Findings

Solutions in Minkowski and Temporal Euclidean spaces are equivalent for ladder QED2+1.

Fermion propagators exhibit confinement due to non-Kallen-Lehmann behavior.

The approach confirms confinement in QCD quark gap equations.

Abstract

Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. QCD quark gap equation is solved in the framework of Temporal Euclidean space as well. In both models, the obtained complex fermion propagators exhibits confinement, since it does not satisfies Khallen-Lehmann representation.