Asymptotic Infrared Fractal Structure of the Propagator for a Charged Fermion
Abstract
It is well known that the longrange 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 gaugeinvariant manner. It has even been suggested that the fractal "anomalous dimension" can be removed by a gauge transformation. Here, a gaugeinvariant nonperturbative calculation will be discussed yielding an unambiguous fractional exponent. The closely analogous case of soft graviton exponents is also briefly explored.
 Publication:

Modern Physics Letters A
 Pub Date:
 2006
 DOI:
 10.1142/S0217732306022316
 arXiv:
 arXiv:hepth/0606003
 Bibcode:
 2006MPLA...21.2861G
 Keywords:

 12.20.m;
 03.70.+k;
 Quantum electrodynamics;
 Theory of quantized fields;
 High Energy Physics  Theory
 EPrint:
 Updated with a corrected sign error, longer discussion of fractal dimension, and more references