S. A. Fulling
Systematics of the Relationship between Vacuum Energy Calculations and 
Heat Kernel Coefficients
(63K, LaTeX (RevTeX 4))

ABSTRACT.  Casimir energy is a nonlocal effect; its magnitude cannot be deduced from 
heat kernel expansions, even those including the integrated boundary 
terms. 
On the other hand, it is known that the divergent terms in the regularized 
(but not yet renormalized) total vacuum energy are associated with the 
heat kernel coefficients. 
Here a recent study of the relations among the eigenvalue density, the 
heat kernel, and the integral kernel of the operator $e^{-t\sqrt{H}}$ is 
exploited to characterize this association completely. 
Various previously isolated observations about the structure of the 
regularized energy emerge naturally. 
For over 20 years controversies have persisted stemming from the fact that 
certain (presumably physically meaningful) terms in the renormalized 
vacuum energy density in the interior of a cavity become singular at the 
boundary and correlate to certain divergent terms in the regularized total 
energy. 
The point of view of the present paper promises to help resolve these 
issues.