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An Abraham-Lorentz-like Equation for the Electron from the Worldline Variational Approach to QED

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.