Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $Q^2$ evolution of Soffer inequality   DGLAP evolution equations may be presented in a form completely analogous to
the Boltzmann equation. This provides a natural proof of the positivity of the
spin-dependent parton distributions, provided the initial distributions at
$Q^2_0$ are also positive. In addition, the evolution to $Q^2 < Q^2_0$ may
violate positivity, providing therefore a 'time arrow'. The positivity
condition is just $|\Delta P_{ij} (z)| \leq P_{ij} (z) $ for $z < 1$ for all
types of partons, while the $'+'$prescription and terms containing
$\delta(1-z)$ do not affect positivity. This method allows one to complete
immediately the existing proof of Soffer inequality at leading and
next-to-leading order.

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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
2
The categories of this paper are: math
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: comp-gas