Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\Delta(1232)$-Resonance in the Hydrogen Spectrum   The electromagnetic excitation of the $\Delta(1232)$-resonance plays an
appreciable role in the Lamb shift and hyperfine structure of muonic and
electronic hydrogen. Its effect appears at the subleading order
$\mathcal{O}(\alpha^5)$, together with other proton-polarizability
contributions from forward two-photon exchange. We use the large-$N_c$
relations for the nucleon-to-delta transition form factors to compute the
effect of the $\Delta(1232)$ in the hydrogen spectrum. We pay particular
attention to a subtile difference between predictions based on a direct
calculation of the two-photon exchange (or Compton scattering amplitudes) and
predictions based on the $\Delta(1232)$-production photoabsorption cross
sections. The mismatch is explained by studying the dispersion relations for
tree-level Compton scattering off the proton in more details.

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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: physics