  Quantum vacuum energy has been known to have observable consequences since
1948 when Casimir calculated the force of attraction between parallel uncharged
plates, a phenomenon confirmed experimentally with ever increasing precision.
Casimir himself suggested that a similar attractive self-stress existed for a
conducting spherical shell, but Boyer obtained a repulsive stress. Other
geometries and higher dimensions have been considered over the years. Local
effects, and divergences associated with surfaces and edges have been
investigated by several authors. Quite recently, Graham et al. have re-examined
such calculations, using conventional techniques of perturbative quantum field
theory to remove divergences, and have suggested that previous self-stress
results may be suspect. Here we show that most of the examples considered in
their work are misleading; in particular, it is well-known that in two
dimensions a circular boundary has a divergence in the Casimir energy for
massless fields, while for general dimension $D$ not equal to an even integer
the corresponding Casimir energy arising from massless fields interior and
exterior to a hyperspherical shell is finite. It has also long been recognized
that the Casimir energy for massive fields is divergent for curved boundaries.
These conclusions are reinforced by a calculation of the relevant leading
Feynman diagram in $D$ dimensions. Divergences do occur in third order, as has
been recognized for many years, but this logarithmic divergence is of
questionable relevance to real shells.
