An Abraham-Lorentz-like equation for the electron from the worldline variational approach to QED
Paul Scherrer Institute, 5232, Villigen PSI, Switzerland
2 Department of Physics and Mathematical Physics, and Research Centre for the Subatomic Structure of Matter, University of Adelaide, S. A. 5005, Adelaide, Australia
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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.
© Springer-Verlag, 2004