Excited by a quantum field: Does shape matter?

TL;DR

This paper demonstrates that a specific regularisation method for the Unruh-DeWitt detector yields a well-defined transition rate in Minkowski space, supporting the idea that the detector profile does not affect the zero-size limit.

Contribution

It introduces a Lorentz-function spatial profile regularisation that ensures a physically reasonable, well-defined transition rate for arbitrarily accelerated detectors.

Findings

Regularisation yields a well-defined transition rate

Results agree with previous stationary case calculations

Supports the conjecture of profile independence in the zero-size limit

Abstract

The instantaneous transition rate of an arbitrarily accelerated Unruh-DeWitt particle detector on four-dimensional Minkowski space is ill defined without regularisation. We show that Schlicht's regularisation as the zero-size limit of a Lorentz-function spatial profile yields a manifestly well-defined transition rate with physically reasonable asymptotic properties. In the special case of stationary trajectories, including uniform acceleration, we recover the results that have been previously obtained by a regularisation that relies on the stationarity. Finally, we discuss evidence for the conjecture that the zero-size limit of the transition rate is independent of the detector profile.