Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ward-Takahashi identity, soft photon theorem and the magnetic moment of
  the $\Delta$ resonance   Starting from the Ward-Takahashi identity for the radiative $\pi N$
scattering amplitude a generalization of the soft photon theorem approach is
obtained for an arbitrary energy of an emitted photon. The external particle
radiation part of the $\pi N\to\gamma'\pi'N' $ amplitude is analytically
reduced to the double $\Delta$ exchange amplitude with the
$\Delta\to\gamma'\Delta'$ vertex function.
  We have shown, that the double $\Delta$ exchange amplitudes with internal
$\Delta$ radiation is connected by current conservation with the corresponding
part of the external particle radiation terms. Moreover according to the
current conservation the internal and external particle radiation terms with
the $\Delta-\gamma'\Delta'$ vertex have a opposite sign i.e. they must cancel
each other.
  Therefore we have a screening of the internal double $\Delta$ exchange
diagram with the $\Delta-\gamma' \Delta'$ vertex by the external particle
radiation. This enables us to obtain a model independent estimation of the
dipole magnetic moment of $\Delta^+$ and $\Delta^{++}$ resonances
$\mu_{\Delta}$ through the anomalous magnetic moment of the proton $\mu_p$ as
$\mu_{\Delta^+}={{M_{\Delta}}\over {m_p}} \mu_p$ and $\mu_{\Delta^{++}}={3\over
2}\mu_{\Delta^+}$ in agreement with the values obtained from the fit of the
experimental cross section of the $\pi^+ p\to\gamma'\pi^+ p$ reaction.

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The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph