We develop a unified approach to both infrared and ultraviolet asymptotics ofthe fermion Green functions in the condensed matter systems that allow for aneffective description in the framework of the Quantum Electrodynamics. Byapplying a path integral representation to the previously suggested form of thephysical electron propagator we demonstrate that in the massless case thisgauge invariant function features a "stronger-than-a-pole" branch-cutsingularity instead of the conjectured Luttinger-like behavior. The obtainedresults alert one to the possibility that construction of physically relevantamplitudes in the effective gauge theories might prove more complex thanpreviously thought.
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