A Zassenhaus-type algorithm solves the Bogoliubov recursion

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dc.creatorEbrahimi-Fard, Kurusch
dc.creatorPatras, Frederic
dc.date2007-10-26
dc.date2007-11-27
dc.date.accessioned2026-07-07T08:44:47Z
dc.date.available2026-07-07T08:44:47Z
dc.descriptionThis paper introduces a new Lie-theoretic approach to the computation of counterterms in perturbative renormalization. Contrary to the usual approach, the devised version of the Bogoliubov recursion does not follow a linear induction on the number of loops. It is well-behaved with respect to the Connes-Kreimer approach: that is, the recursion takes place inside the group of Hopf algebra characters with values in regularized Feynman amplitudes. (Paradigmatically, we use dimensional regularization in the minimal subtraction scheme, although our procedure is generalizable to other schemes.) The new method is related to Zassenhaus' approach to the Baker-Campbell-Hausdorff formula for computing products of exponentials. The decomposition of counterterms is parametrized by a family of Lie idempotents known as the Zassenhaus idempotents. It is shown, inter alia, that the corresponding Feynman rules generate the same algebra as the graded components of the Connes-Kreimer beta-function. This further extends previous work of ours (together with Jose M. Gracia-Bondia) on the connection between Lie idempotents and renormalization procedures, where we constructed the Connes-Kreimer beta-function by means of the classical Dynkin idempotent.
dc.description11 pages, improved version, to appear in Lie Theory and Its Applicatons in Physics VII ed. V.K. Dobrev et al., Heron Press, Sofia, 2008
dc.identifierhttps://arxiv.org/abs/0710.5134
dc.identifierhttp://arxiv.org/abs/0710.5134
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142780
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectCombinatorics
dc.titleA Zassenhaus-type algorithm solves the Bogoliubov recursion
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