Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Off-Shell Yang-Mills Amplitude in the CHY Formalism   M\"obius invariance is used to construct gluon tree amplitudes in the
Cachazo, He, and Yuan (CHY) formalism. If it is equally effective in steering
the construction of off-shell tree amplitudes, then the S-matrix CHY theory can
be used to replace the Lagrangian Yang-Mills theory. In the process of
investigating this possibility, we find that the CHY formula can indeed be
modified to obtain a M\"obius invariant off-shell amplitude, but unfortunately
this modified amplitude $M_P$ is not the Yang-Mills amplitude because it lacks
gauge invariance. A complementary amplitude $M_Q$ must be added to restore
gauge invariance, but its construction relies on the Lagrangian and not
M\"obius invariance. Although neither $M_P$ nor $M_Q$ is fully gauge invariant,
both are partially gauge invariant in a sense to be explained. This partial
gauge invariance turns out to be very useful for checking calculations. A
Feynman amplitude so split into the sum of $M_P$ and $M_Q$ also contains fewer
terms.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: physics
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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: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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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: quant-ph