Proof of the Bogoliubov-Parasiuk theorem on renormalization

Hepp, K.

doi:10.1007/bf01773358

Cited by 682 publications

(577 citation statements)

References 9 publications

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“…In principle, it should be possible to implement in position space a natural variant of the BPHZ renormalization procedure [14,15,16]; the R-operation is a rather general method for subtracting divergences, whose mechanism is quite insensitive to the particular prescription for the subtractions. Moreover, it might be possible to adapt the reformulation of the BPHZ procedure in terms of Hopf algebras, due to Kreimer [17].…”

Section: Discussionmentioning

confidence: 99%

Non Local Theories: New Rules for Old Diagrams

Piacitelli¹

2004

J. High Energy Phys.

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Abstract:We show that a general variant of the Wick theorems can be used to reduce the time ordered products in the Gell-Mann & Low formula for a certain class on non local quantum field theories, including the case where the interaction lagrangian is defined in terms of twisted products. The only necessary modification is the replacement of the Stueckelberg-Feynman propagator by the general propagator (the "contractor" of Denk and Schweda)where the violations of locality and causality are represented by the dependence of τ, τ on other points, besides those involved in the contraction. This leads naturally to a diagrammatic expansion of the Gell-Mann & Low formula, in terms of the same diagrams as in the local case, the only necessary modification concerning the Feynman rules. The ordinary local theory is easily recovered as a special case, and there is a one-to-one correspondence between the local and non local contributions corresponding to the same diagrams, which is preserved while performing the large scale limit of the theory.

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Section: Discussionmentioning

confidence: 99%

Non Local Theories: New Rules for Old Diagrams

Piacitelli¹

2004

J. High Energy Phys.

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“…Any such approach must confront three main issues: spurious phase space singularities that appear during the reduction of tensor integrals, the extraction of soft and collinear singularities, and the presence of internal thresholds where analytic continuation is required. An approach that addresses the first two issues exists, called sector decomposition [9,10,11]. It permits a completely automated, numerical extraction of infrared singularities from loop integrals.…”

Section: Introductionmentioning

confidence: 99%

QCD corrections to triboson production

2007

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We present a computation of the next-to-leading order QCD corrections to the production of three Z bosons at the LHC. We calculate these corrections using a completely numerical method that combines sector decomposition to extract infrared singularities with contour deformation of the Feynman parameter integrals to avoid internal loop thresholds. The NLO QCD corrections to pp → ZZZ are approximately 50%, and are badly underestimated by the leading order scale dependence. However, the kinematic dependence of the corrections is minimal in phase space regions accessible at leading order.

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“…This was achieved, by Bogoliubov, Parasiuk, Hepp, Zimmermann, Epstein, Glaser, Steinmann and others, in a twenty years struggle, and the finally reached state of the art is nicely documented in the proceedings of the Erice school 1975 dedicated to renormalization [VW76]. Main highlights are the Forest Formula of Zimmermann [Zim69] which solves the recursion relations of the Bogoliubov-Parasiuk-Hepp (BPH) method [BP57,BS59,Hep66], the causal method of Epstein-Glaser (EG) [EG73], elaborating on older attempts of Stückelberg [SR50] and Bogoliubov [BP57,BS59], and the method of retarded products by Steinmann [Ste71].…”

Section: Introductionmentioning

confidence: 99%

Dimensional regularization in position space and a Forest Formula for Epstein-Glaser renormalization

Dütsch¹,

Fredenhagen²,

Keller³

et al. 2014

Journal of Mathematical Physics

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We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of Epstein-Glaser. This closed expression, which we call the Epstein-Glaser Forest Formula, is analogous to Zimmermann's Forest Formula for BPH renormalization. For scalar fields the resulting renormalization method is always applicable, we compute several examples. We also analyze the Hopf algebraic aspects of the combinatorics. Our starting point is the Main Theorem of Renormalization of Stora and Popineau and the arising renormalization group as originally defined by Stückelberg and Petermann.

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Proof of the Bogoliubov-Parasiuk theorem on renormalization

Cited by 682 publications

References 9 publications

Non Local Theories: New Rules for Old Diagrams

Non Local Theories: New Rules for Old Diagrams

QCD corrections to triboson production

Dimensional regularization in position space and a Forest Formula for Epstein-Glaser renormalization

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