Gauge (non)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 the 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.

fermion: Dirac
gauge field theory
condensed matter
quantum electrodynamics
path integral
electron: propagator

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