Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirac Quantization Condition Holds with Nonzero Photon Mass   Dirac in 1931 gave a beautiful argument for the quantization of electric
charge, which required only the existence in the universe of one magnetic
monopole, because gauge invariance of the interaction between the pole and any
charge could hold only if the product of the charge and the pole strength were
quantized in half-integer multiples of the reduced Planck constant. However, if
the photon had a nonzero mass, implying exponential decrease of the flux out of
an electric charge, then Dirac's argument might seem to fail. We demonstrate
that the result still should hold. The key point is that magnetic charge,
unlike electric charge, cannot be screened, so that on any surface enclosing
the pole Dirac's string, or equally the Wu-Yang gauge shift, must be present,
and to make either of these invisible to charged particles the quantization
condition is required.

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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: math
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph