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Worldline Influence Functional: Abraham-Lorentz-Dirac-Langevin Equation from QED

Philip R. Johnson·B. L. Hu
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Abstract

We present a stochastic theory of charges moving in an electromagnetic field using nonequilibrium quantum field theory. We give a first principles' derivation of the Abraham-Lorentz-Dirac-Langevin equation which depicts the quantum expectation value for a particle's trajectory and its stochastic fluctuations by combining the worldline path integral quantization with the Feynman-Vernon influence functional or closed-time-path effective action methods. At lowest order, the equations of motion are approximated by a stochastic Lorentz-Dirac equation.

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Philip R. Johnson, B. L. Hu. 2000-12-22. Worldline Influence Functional: Abraham-Lorentz-Dirac-Langevin Equation from QED. https://arxiv.org/abs/quant-ph/0012135

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