The fermion propagator is studied in the whole Minkowski space with the help of the Schwinger-Dyson equations. Various integral representations are employed to get solutions for the dynamical breaking of chiral symmetry in different regimes of the coupling constant. In particular, in the case of massive boson, we extend the singularity structure of the fermion propagator to the two real pole Ansätze.

• Received 20 July 2006

DOI:https://doi.org/10.1103/PhysRevD.75.087701