Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: SU(2) low energy quark effective couplings in weak external magnetic
  field   In this work corrections to the usual flavor SU(2) Nambu-Jona-Lasinio
coupling due to a weak external magnetic field are calculated by considering
quark polarization in a (dressed) gluon exchange mechanism for quark
interactions. The quark field is splitted into two components, one that
condenses and another one that is a background field for interacting quarks,
being the former integrated out. The resulting determinant is expanded for
relatively large quark mass and small magnetic field, $(eB_0/{M^*}^2)<1$ by
resolving magnetic field dependent low energy quark effective interactions.
Besides the corrections for the NJL and vector NJL effective couplings,
different $B_0-$dependent effective couplings that break isospin and chiral
symmetry emerge.

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The categories of this paper are: econ
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The categories of this paper are: physics
8
The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol