Fractal Propagators in QED and QCD and Implications for the Problem of Confinement

TL;DR

This paper explores how radiative corrections in QED and gravitational effects in QCD influence particle propagators, suggesting a fractal trajectory approach to understanding confinement phenomena.

Contribution

It introduces a novel perspective on confinement in QCD through fractal dimensions of particle trajectories influenced by quantum corrections.

Findings

QED corrections induce fractional anomalous exponents in propagators

Gravitational effects modify non-abelian field behaviors

Proposes a fractal dimension approach to confinement in QCD

Abstract

We show that QED radiative corrections change the propagator of a charged Dirac particle so that it acquires a fractional anomalous exponent connected with the fine structure constant. The result is a nonlocal object which represents a particle with a roughened trajectory whose fractal dimension can be calculated. This represents a significant shift from the traditional Wigner notions of asymptotic states with sharp well-defined masses. Non-abelian long-range fields are more difficult to handle, but we are able to calculate the effects due to Newtonian gravitational corrections. We suggest a new approach to confinement in QCD based on a particle trajectory acquiring a fractal dimension which goes to zero in the infrared as a consequence of self-interaction, representing a particle which, in the infrared limit, cannot propagate.