Sudden vector-potential pulse

In temporal gauge, a spatially uniform step $\mathbf{A}(t)={\mathbf{A}}_0\Theta (t)$ gives $\mathbf{E}=-{\mathbf{A}}_0\delta (t)$. A charged scalar Fourier mode retains its canonical wavevector while its kinetic momentum changes from $\hslash \mathbf{k}$ to $\hslash \mathbf{k}-e{\mathbf{A}}_0$. The resulting frequency jump mixes positive- and negative-frequency modes.