Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Casimir Energy of the Universe and New Regularization of Higher
  Dimensional Quantum Field Theories   Casimir energy is calculated for the 5D electromagnetism and 5D scalar theory
in the {\it warped} geometry. It is compared with the flat case. A new
regularization, called {\it sphere lattice regularization}, is taken. In the
integration over the 5D space, we introduce two boundary curves (IR-surface and
UV-surface) based on the {\it minimal area principle}. It is a {\it direct}
realization of the geometrical approach to the {\it renormalization group}. The
regularized configuration is {\it closed-string like}. We do {\it not} take the
KK-expansion approach. Instead, the position/momentum propagator is exploited,
combined with the {\it heat-kernel method}. All expressions are closed-form
(not KK-expanded form). The {\it generalized} P/M propagators are introduced.
We numerically evaluate $\La$(4D UV-cutoff), $\om$(5D bulk curvature, warp
parameter) and $T$(extra space IR parameter) dependence of the Casimir energy.
We present two {\it new ideas} in order to define the 5D QFT: 1) the summation
(integral) region over the 5D space is {\it restricted} by two minimal surfaces
(IR-surface, UV-surface) ; or 2) we introduce a {\it weight function} and
require the dominant contribution, in the summation, is given by the {\it
minimal surface}. Based on these, 5D Casimir energy is {\it finitely} obtained
after the {\it proper renormalization procedure.} The {\it warp parameter}
$\om$ suffers from the {\it renormalization effect}. The IR parameter $T$ does
not. We examine the meaning of the weight function and finally reach a {\it new
definition} of the Casimir energy where {\it the 4D momenta(or coordinates) are
quantized} with the extra coordinate as the Euclidean time (inverse
temperature). We examine the cosmological constant problem and present an
answer at the end. Dirac's large number naturally appears.

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The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol