  One of J. Stuart Dowker's most significant achievements has been to observe
that the theory of diffraction by wedges developed a century ago by Sommerfeld
and others provided the key to solving two problems of great interest in
general-relativistic quantum field theory during the last quarter of the
twentieth century: the vacuum energy associated with an infinitely thin,
straight cosmic string, and (after an interchange of time with a space
coordinate) the apparent vacuum energy of empty space as viewed by an
accelerating observer. In a sense the string problem is more elementary than
the wedge, since Sommerfeld's technique was to relate the wedge problem to that
of a conical manifold by the method of images. Indeed, Minkowski space, as well
as all cone and wedge problems, are related by images to an infinitely sheeted
master manifold, which we call Dowker space. We review the research in this
area and exhibit in detail the vacuum expectation values of the energy density
and pressure of a scalar field in Dowker space and the cone and wedge spaces
that result from it. We point out that the (vanishing) vacuum energy of
Minkowski space results, from the point of view of Dowker space, from the
quantization of angular modes, in precisely the way that the Casimir energy of
a toroidal closed universe results from the quantization of Fourier modes; we
hope that this understanding dispels any lingering doubts about the reality of
cosmological vacuum energy.
