#### Abstract

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.

#### Keywords

Coulomb interaction, high energy physics theory, asymptotic infrared fractal structure

#### Subject Categories

Quantum field theory, Particles (Nuclear physics), Fermions

#### Disciplines

Physics

#### Publication Date

2006

#### Permanent URL

#### Recommended Citation

Gulzari, S.; Swain, J.; and Widom, A., "Asymptotic infrared fractal structure of the propagator for a charged fermion" (2006). *Physics Faculty Publications.* Paper 33. http://hdl.handle.net/2047/d20000386

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## Notes

Originally posted at http://arxiv.org/abs/hep-th/0606003v2. Preprint of an article published in Modern Physics Letters A, 2006.