  The influence functional is derived for a massive scalar field in the ground
state, coupled to a uniformly accelerating DeWitt monopole detector in $D+1$
dimensional Minkowski space. This confirms the local nature of the Unruh
effect, and provides an exact solution to the problem of the accelerating
detector without invoking a non-standard quantization. A directional detector
is presented which is efficiently decohered by the scalar field vacuum, and
which illustrates an important difference between the quantum mechanics of
inertial and non-inertial frames. From the results of these calculations, some
comments are made regarding the possibility of establishing a quantum
equivalence principle, so that the Hawking effect might be derived from the
Unruh effect.
