= Ultraviolet divergence of an instantaneous vector-potential quench
{title2=$|v_{\mathbf k}|^2=O(k^{-2})$}
For a nonzero instantaneous homogeneous vector-potential step, scalar-field mixing has $|v_{\mathbf k}|^2\sim[e\mathbf A_0\cdot\widehat{\mathbf k}]^2/(4\hbar^2k^2)$ at large <wavevector>. Its three-dimensional momentum integral diverges. Per-mode squeezed-state formulas remain meaningful, but at finite quantization volume the mode product needs an ultraviolet regulator or a sufficiently smooth physical pulse. Infinite-volume representations require a separate limit.
Back to article page
