Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vacuum Energy and Casimir Force in a Presence of Skin-depth Dependent
  Boundary Condition   The vacuum energy-momentum tensor (EMT) and the vacuum energy corresponding
to massive scalar field on $\Re_{t}\times [0,l] \times \Re^{D-2}$ space-time
with boundary condition involving a dimensional parameter ($\delta$) are found.
The dependent on the cavity size $l$ Casimir energy $\wt E_{C}$ is a uniquely
determinable function of mass $m$, size $l$ and "skin-depth" $\delta$. This
energy includes the "bulk" and the surface (potential energy) contributions.
The latter dominates when $l \sim \delta$. Taking the surface potential energy
into account is crucial for the coincidence between the derivative $-\d \wt
E_{C}/\d l$ and the $ll$-component of the vacuum EMT. Casimir energy $\wt E_C$
and the bulk contribution to it are interconnected through Legendre
transformation, in which the quantity $\delta^{-1}$ is conjugate to the vacuum
surface energy multiplied by $\delta$. The surface singularities of the vacuum
EMT do not depend on $l$ and, for even $D$, $\delta =0$ or $\infty$, possess
finite interpretation. The corresponding vacuum energy is finite and retains
known analytical dependence on the dimension $D$.

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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
16
The categories of this paper are: stat
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org