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- W3105348077 abstract "It is easy to sum chain-free self-energy rainbows, to obtain contributions to anomalous dimensions. It is also easy to resum rainbow-free self-energy chains. Taming the combinatoric explosion of all possible nestings and chainings of a primitive self-energy divergence is a much more demanding problem. We solve it in terms of the coproduct $Delta$, antipode S, and grading operator Y of the Hopf algebra of undecorated rooted trees. The vital operator is $Sstar Y$, with a star product effected by $Delta$. We perform 30-loop Pad'e-Borel resummation of 463 020 146 037 416 130 934 BPHZ subtractions in Yukawa theory, at spacetime dimension d=4, and in a trivalent scalar theory, at d=6, encountering residues of $Sstar Y$ that involve primes with up to 60 digits. Even with a very large Yukawa coupling, g=30, the precision of resummation is remarkable; a 31-loop calculation suggests that it is of order $10^{-8}$." @default.
- W3105348077 created "2020-11-23" @default.
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- W3105348077 date "2000-02-01" @default.
- W3105348077 modified "2023-10-17" @default.
- W3105348077 title "Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Padé-Borel resummation" @default.
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- W3105348077 doi "https://doi.org/10.1016/s0370-2693(00)00051-4" @default.
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