Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalization Group Equations in Gauge Theories with Multiple U(1)
  Groups   Two-loop renormalization group equations in gauge theories with multiple U(1)
groups are presented. Instead of normalizing the abelian gauge fields in
canonical forms, we retain kinetic-mixing terms and treat the mixing
coefficients as free parameters. The beta- and gamma-functions are then
obtained in a straightforward manner.

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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: math
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga