Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalization Group Approach to Casimir Effect and the Attractive and
  Repulsive Forces in Substance   Electromagnetism in substance is characterized by permittivity (dielectric
constant) and permeability (magnetic permeability). They describe the substance
property {\it effectively}. We present a {\it geometric} approach to it. Some
models are presented, where the two quantities are geometrically defined.
Fluctuation due to the micro dynamics (such as dipole-dipole interaction) is
taken into account by the (generalized) path-integral. Free energy formula
(Lifshitz 1954), for the material composed of three regions with different
permittivities, is explained. Casimir energy is obtained by a new
regularization using the path-integral. Attractive force or repulsive one is
determined by the sign of the {\it renormalization-group} $\beta$-function.

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The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org