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Transmutation operators and expansions for $1$-loop Feynman integrands | | Kang Zhou
; | | Date: |
5 Jan 2022 | | Abstract: | In this paper, the connections among $1$-loop Feynman integrands of a large
variety of theories with massless external states are further investigated. The
work includes two parts. First, we construct a new class of differential
operators which transmute the $1$-loop gravitational Feynman integrands to
$1$-loop Yang-Mills Feynman integrands. The new operators are commutable with
the integration of loop momentum, thus the corresponding transmutational
relation holds at not only the integrands level, but also the $1$-loop
amplitude level. Secondly, by using $1$-loop level transmutational relations,
together with some general requirements such as gauge and Lorentz invariance,
we derive the expansions of the Feynman integrands of one theory to those of
other theories. The unified web of expansions is established, including a wide
range of theories which are gravitational theory, Einstein-Yang-Mills theory,
Einstein-Maxwell theory, Born-Infeld theory, pure Yang-Mills theory,
Yang-Mills-scalar theory, special Yang-Mills theory, Dirac-Born-Infeld theory,
extended Dirac-Born-Infeld theory, special Galileon theory, non-linear sigma
model. The systematic rules for evaluating coefficients in the expansions are
provided, and the duality between transmutational relations and expansions is
shown. | | Source: | arXiv, 2201.01552 | | Services: | Forum | Review | PDF | Favorites | |
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