Confinement, Chiral Symmetry Breaking and complex mass in QED2+1 in Minkowski and Euclidean spaces

TL;DR

This paper solves ladder QED2+1 directly in Minkowski space and demonstrates the equivalence of solutions in Minkowski and Temporal Euclidean spaces, revealing confinement through a complex fermion propagator without real poles.

Contribution

It provides the first direct Minkowski space solution of ladder QED2+1 and establishes the equivalence with Euclidean space results, highlighting confinement mechanisms.

Findings

Fermion propagator is complex, indicating confinement.

Solutions in Minkowski and Euclidean spaces are equivalent.

No real poles in the fermion propagator, confirming confinement.

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. The obtained complex fermion propagator exhibits confinement because of the lack of the pole at the real timelike $q^2$ axis.