Corrections to the Unruh Effect from Robin Boundary Conditions in Punctured Minkowski Spacetime

Abstract

We consider a real massless scalar field in punctured Minkowski spacetime, endowed at the removed origin with the stable one-parameter family of Robin boundary conditions $G(0)-βG'(0)=0$, $β\geq0$. We obtain the boundary-induced part of the static ground-state Wightman function in closed form and study the response of a uniformly accelerated Unruh-DeWitt detector. The puncture breaks the boost symmetry underlying the stationary Unruh response, so the boundary-induced pullback is nonstationary in proper time. The corresponding subtracted detector contribution can either enhance or suppress the ordinary Minkowski response and depends on the Robin parameter, the detector gap, and the portion of the trajectory sampled. For the unshifted, radially aligned trajectory studied in detail, we prove that the boundary-induced pullback is absolutely integrable in the two proper-time variables. Consequently, as the smooth interaction is extended over the full detector history, this contribution approaches a finite limit and remains $O(1)$, producing no additional term linear in the interaction duration. The formal Neumann limit is singular: the boundary-induced two-point function grows logarithmically because of an infrared singularity in the $s$-wave sector, and the numerical response exhibits growth consistent with this asymptotic behavior.