 0360 S. A. Fulling
 Systematics of the Relationship between Vacuum Energy Calculations and
Heat Kernel Coefficients
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Feb 14, 03

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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.
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