Regularization versus renormalization: Why are Casimir energy differences so often finite?

Understand

One of the very first applications of the quantum field theoretic vacuum state was in the development of the notion of Casimir energy.

• Now field theoretic Casimir energies, considered individually, are always infinite.
• But differences in Casimir energies (at worst regularized, not renormalized) are quite often finite --- a fortunate circumstance which luckily made some of the early calculations, (for instance, for parallel plates and hollow spheres), tolerably tractable.
• We shall explore the extent to which this observation can be made systematic.