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

S. Gulzari·Y. N. Srivastava·J. Swain·A. Widom
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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.

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S. Gulzari, Y. N. Srivastava, J. Swain, A. Widom. 2006-12-09. Fractal Propagators in QED and QCD and Implications for the Problem of Confinement. https://doi.org/10.1590/s0103-97332007000200021

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