Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three easy exercises in off-shell string-inspired methods   Off-shell string-inspired methods (OSSIM) calculate off-shell QCD Green's
functions using Schwinger-Feynman proper-time techniques, always in the
background field method (BFM) Feynman gauge for technical convenience, and so
far only at one loop. We already know that these results are gauge-invariant,
because this gauge realizes the prescriptions of the Pinch Technique (PT), a
Feynman-graph formulation for any gauge, but the idea of the first exercise is
to show this directly in OSSIM. In this exercise we extend proper-time OSSIM
beyond the BFM Feynman gauge so that one can apply PT algorithms, and show that
the intrinsic PT is equivalent to resolving ambiguities in OSSIM in other
gauges. In the second exercise we use forty-year-old rules of the author and
Tiktopoulos for expressing loop integrals with numerator momenta directly in
terms of Feynman parameters after momentum integration (the goal of OSSIM) and
show that these rules elegantly and with economy of effort give rise, at least
at one loop, to standard OSSIM algorithms. In the third exercise we apply
world-line techniques to the problem of the breaking of adjoint strings,
requiring a non-perturbative treatment that in the end reduces to a variant of
the Schwinger result for production of electron-positron pairs in an electric
field. This generalizes OSSIM to non-perturbative processes.

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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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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: quant-ph