Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Casimir Energy for concentric $\delta$-$\delta'$ spheres   We study the vacuum interaction of a scalar field and two concentric spheres
defined by a singular potential on their surfaces. The potential is a linear
combination of the Dirac-$\delta$ and its derivative. The presence of the delta
prime term in the potential causes that it behaves differently when it is seen
from the inside or from the outside of the sphere. We study different cases for
positive and negative values of the delta prime coupling, keeping positive the
coupling of the delta. As a consequence, we find regions in the space of
couplings, where the energy is positive, negative or zero. Moreover, the sign
of the $\delta'$ couplings cause different behavior on the value of the Casimir
energy for different values of the radii. This potential gives rise to general
boundary conditions with limiting cases defining Dirichlet and Robin boundary
conditions what allows us to simulate purely electric o purely magnetic
spheres.

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The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: math
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: physics