Smooth and sharp creation of a pointlike source for a $(3+1)$-dimensional quantum field

We analyse the smooth and sharp creation of a pointlike source for a quantised massless scalar field in $(3+1)$-dimensional Minkowski spacetime, as a model for the breakdown of correlations that has been proposed to occur at the horizon of an evaporating black hole. The creation is implemented by a time-dependent self-adjointness parameter at the excised spatial origin. In a smooth creation, the renormalised energy density $\langle T_{00} \rangle$ is well defined away from the source, but it is unbounded both above and below: the outgoing pulse contains an infinite negative energy, while a cloud of infinite positive energy lingers near the fully-formed source. In the sharp creation limit, $\langle T_{00} \rangle$ diverges everywhere in the timelike future of the creation event, and so does the response of an Unruh-DeWitt detector that operates in the timelike future of the creation event. The source creation is significantly more singular than the corresponding process in $1+1$ dimensions, analysed previously, and it may be sufficiently singular to break quantum correlations as proposed in a black hole spacetime.