Kinetic Theory and Stochastic Simulation of Field Quanta

We develop quantum electrodynamics into a kinetic-theory-like evolution equation for electrons, positrons and photons. To keep the "collision rules" simple, we make use of longitudinal and temporal photons in addition to the usual transverse photons. For our explicitly time-dependent approach, we introduce proper time-correlation functions. We then develop a stochastic simulation technique for solving the resulting kinetic equation and we comment on the subtleties associated with gauge invariance, Lorentz invariance and divergent integrals. To illustrate the validity and power of the proposed ideas, we show how a very simple simulation of the dynamics of field quanta can be used to obtain the main contribution to the anomalous magnetic moment of the electron.