Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Systematics of the Relationship between Vacuum Energy Calculations and
  Heat Kernel Coefficients   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.

30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph