Gauge-invariant Green functions of Dirac fermions coupled to gauge fields

We develop a unified approach to both infrared and ultraviolet asymptotics of the fermion Green functions in the condensed-matter systems that allow for an effective description in the framework of quantum electrodynamics. By applying a path-integral representation to the previously suggested form of the physical electron propagator we demonstrate that in the massless case this gauge-invariant function features a ``stronger-than-a-pole'' branch-cut singularity instead of the conjectured Luttinger-like behavior. The obtained results alert one to the possibility that construction of physically relevant amplitudes in the effective gauge theories might prove more complex than previously thought.