Worldline influence functional : Abraham-Lorentz-Dirac-Langevin equation from QED

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 [1, 2]. At lowest order, the equations of motion are approximated by a stochastic Lorentz-Dirac equation.