Infrared asymptotic behavior of gauge-invariant propagator in quantum electrodynamics

A new class of gauge-invariant fields is introduced. For the gauge-invariant propagator of a spinor field the analogue of the Dyson–Schwinger equations is derived. With the help of these equations as well as the functional integration method it is shown that the gauge-invariant spinor propagator has a simple pole singularity in the infrared region.