  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.
