Chiral Symmetry Breaking and confinement in Minkowski space QED2+1

TL;DR

This paper solves ladder QED2+1 directly in Minkowski space, demonstrating confinement through complex fermion propagators and establishing equivalence with solutions in Temporal Euclidean space, challenging the validity of Wick rotation.

Contribution

It provides a direct Minkowski space solution for ladder QED2+1 and compares it with Euclidean approaches, highlighting confinement and the limitations of Wick rotation.

Findings

Fermion propagator has no pole, indicating confinement.

Minkowski and Temporal Euclidean solutions are equivalent.

Infrared dynamical mass aligns with other approaches.

Abstract

Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Obtained complex fermion propagator exhibits confinement in the sense that it has no pole. 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. Obvious invalidity of Wick rotation is briefly discussed. The infrared value of the dynamical mass is compared with other known approaches, e.g. with the standard Euclidean calculation.