Convergence of Bogoliubov's method of renormalization in momentum space

Zimmermann, W.

doi:10.1007/bf01645676

Cited by 534 publications

(517 citation statements)

References 13 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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“…A (correct) proof of the validity of Bogoliubov's method was finally given by Hepp [18] in 1966 and by Zimmermann [32] in 1969.…”

Section: The Extension Of Distributionsmentioning

confidence: 98%

“…(17), we expandS(q) and renormalization constants over trees using Eqs. (23), (31), (32) and (33). We replace products by convolutions ∇ according to Eq.…”

Section: The Renormalized Electron Propagatormentioning

confidence: 99%

Renormalization of QED with planar binary trees

Brouder

Frabetti

2001

Eur. Phys. J. C

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Abstract. The renormalized photon and electron propagators are expanded over planar binary trees. Explicit recurrence solutions are given for the terms of these expansions. In the case of massless Quantum Electrodynamics (QED), the relation between renormalized and bare expansions is given in terms of a Hopf algebra structure. For massive quenched QED, the relation between renormalized and bare expansions is given explicitly.

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“…Classical perturbation theory, like the inductive solution of any deterministic equation, is indexed by trees, whether QFT perturbation theory is indexed by more complicated "Feynman graphs", which contain the famous "loops" of anti-particles responsible for the ultraviolet divergences 5 . But the classical trees hidden inside QFT were revealed in many steps, starting with Zimmermann (which called them forests...) [18] through Gallavotti and many others, until Kreimer and Connes viewed them as generators of Hopf algebras [19,20,21]. Roughly speaking the trees were hidden because they are not just subgraphs of the Feynman graphs.…”

Section: Arxiv:07050705v1 [Hep-th] 4 May 2007mentioning

confidence: 99%

Non-commutative Renormalization

Rivasseau

2007

Quantum Spaces

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Abstract. A new version of scale analysis and renormalization theory has been found on the non-commutative Moyal space. It could be useful for physics beyond the standard model or for standard physics in strong external field. The good news is that quantum field theory is better behaved on non-commutative than on ordinary space: indeed it has no Landau ghost. Noncommutativity might therefore be an alternative to supersymmetry. We review this rapidly growing subject.

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Convergence of Bogoliubov's method of renormalization in momentum space

Abstract: Bogoliubov's method of renormalization is formulated in momentum space. The convergence of the renormalized Feynman integrand is proved by an application of the power counting theorem.

Cited by 534 publications

References 13 publications

Non Local Theories: New Rules for Old Diagrams

Non Local Theories: New Rules for Old Diagrams

Renormalization of QED with planar binary trees

Non-commutative Renormalization

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