  The variational equation for the mean square displacement of the electron in
the polaron worldline approach to quenched QED can be cast into a form which
closely resembles the classical Abraham-Lorentz equation but without the
conceptual and practical diseases of the latter. The connection with delay
equations describing field retardation effects is also established. As
applications we solve this integro-differential equation numerically for
various values of the coupling constant and cut-off and re-derive the
variational approximation to the anomalous mass dimension of the electron found
recently.
