Abstract
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.
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