It is well known that the long-range nature of the Coulomb interaction makes the definition of asymptotic "in" and "out" states of charged particles problematic in quantum field theory. In particular, the notion of a simple particle pole in the vacuum charged particle propagator is untenable and should be replaced by a more complicated branch cut structure describing an electron interacting with a possibly infinite number of soft photons. Previous work suggests a Dirac propagator raised to a fractional power dependent upon the fine structure constant, however the exponent has not been calculated in a unique gauge-invariant manner. It has even been suggested that the fractal "anomalous dimension" can be removed by a gauge transformation. Here, a gauge-invariant non-perturbative calculation will be discussed yielding an unambiguous fractional exponent. The closely analogous case of soft graviton exponents is also briefly explored.
ASYMPTOTIC INFRARED FRACTAL STRUCTURE OF THE PROPAGATOR FOR A CHARGED FERMION
