Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cooper pairing reexamined   When both two-electron \textit{and} two-hole Cooper-pairing are treated on an
equal footing in the ladder approximation to the Bethe-Salpeter (BS) equation,
the zero-total-momentum Cooper-pair energy is found to have two \textit{real}
solutions $\mathcal{E}_{0}^{BS}=\pm 2\hbar \omega_{{D}%}/\sqrt{{e}^{2/\lambda
}+{1}}$ which coincide with the zero-temperature BCS energy gap $\Delta =\hbar
\omega_{D}/\sinh (1/\lambda) $ in the weak coupling limit. Here, $\hbar
\omega_{D}$ is the Debye energy and $\lambda \geq 0$ the BCS model interaction
coupling parameter. The interpretation of the BCS energy gap as the binding
energy of a Cooper-pair is often claimed in the literature but, to our
knowledge, never substantiated even in weak-coupling as we find here. In
addition, we confirm the two purely-\textit{imaginary} solutions assumed since
at least the late 1950s as the \textit{only} solutions, namely,
$\mathcal{E}_{0}^{BS}=\pm i2\hbar \omega_{{D}}/\sqrt{{e}^{2/\lambda}{-1}}.$

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: math
3
The categories of this paper are: physics
18
The categories of this paper are: econ
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
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The categories of this paper are: eess
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th