  From the beginning of the subject, calculations of quantum vacuum energies or
Casimir energies have been plagued with two types of divergences: The total
energy, which may be thought of as some sort of regularization of the
zero-point energy, $\sum\frac12\hbar\omega$, seems manifestly divergent. And
local energy densities, obtained from the vacuum expectation value of the
energy-momentum tensor, $\langle T_{00}\rangle$, typically diverge near
boundaries. The energy of interaction between distinct rigid bodies of whatever
type is finite, corresponding to observable forces and torques between the
bodies, which can be unambiguously calculated. The self-energy of a body is
less well-defined, and suffers divergences which may or may not be removable.
Some examples where a unique total self-stress may be evaluated include the
perfectly conducting spherical shell first considered by Boyer, a perfectly
conducting cylindrical shell, and dilute dielectric balls and cylinders. In
these cases the finite part is unique, yet there are divergent contributions
which may be subsumed in some sort of renormalization of physical parameters.
The divergences that occur in the local energy-momentum tensor near surfaces
are distinct from the divergences in the total energy, which are often
associated with energy located exactly on the surfaces. However, the local
energy-momentum tensor couples to gravity, so what is the significance of
infinite quantities here? For the classic situation of parallel plates there
are indications that the divergences in the local energy density are consistent
with divergences in Einstein's equations; correspondingly, it has been shown
that divergences in the total Casimir energy serve to precisely renormalize the
masses of the plates, in accordance with the equivalence principle.
