Time-dependent charge renormalization procedure in QED

We examine the formation process of the vacuum polarization cloud around a localized charge with space-time resolution permitting us to view the traditional charge renormalization procedure from a dynamical perspective. The asymptotic steady-state charge cloud found in the long-time limit (after the subtraction of a suitable term) matches the distribution predicted by standard perturbative propagator techniques based on Feynman diagrams. This match demonstrates that an alternative (classical-field approximation based) approach can predict the nonlinear properties of the vacuum state. It turns out that some aspects of the polarization dynamics suggest that the vacuum can be viewed as a classical dielectric medium, while other aspects are purely quantum mechanical in nature and cannot be predicted from the Maxwell theory for classical fields.