Asymptotic infrared fractal structure of the propagator for a charged fermion
Originally posted at http://arxiv.org/abs/hep-th/0606003v2. Preprint of an article published in Modern Physics Letters A, 2006.
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 nonperturbative calculation will be discussed yielding an unambiguous fractional exponent. The closely analogous case of soft graviton exponents is also briefly explored.
S. Gulzari, J. Swain, and A. Widom. "Asymptotic infrared fractal structure of the propagator for a charged fermion" 2006
Available at: http://works.bepress.com/jswain/7