Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The proximity force approximation for the Casimir energy as a derivative
  expansion   The proximity force approximation (PFA) has been widely used as a tool to
evaluate the Casimir force between smooth objects at small distances. In spite
of being intuitively easy to grasp, it is generally believed to be an
uncontrolled approximation. Indeed, its validity has only been tested in
particular examples, by confronting its predictions with the next to leading
order (NTLO) correction extracted from numerical or analytical solutions
obtained without using the PFA. In this article we show that the PFA and its
NTLO correction may be derived within a single framework, as the first two
terms in a derivative expansion. To that effect, we consider the Casimir energy
for a vacuum scalar field with Dirichlet conditions on a smooth curved surface
described by a function $\psi$ in front of a plane. By regarding the Casimir
energy as a functional of $\psi$, we show that the PFA is the leading term in a
derivative expansion of this functional. We also obtain the general form of
corresponding NTLO correction, which involves two derivatives of $\psi$. We
show, by evaluating this correction term for particular geometries, that it
properly reproduces the known corrections to PFA obtained from exact
evaluations of the energy.

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The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
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The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph