Tree quantum field theory

• Verfasst von: Gurǎu, Rǎzvan [VerfasserIn]
• Verfasst von: Magnen, Jacques [VerfasserIn]
• Verfasst von: Rivasseau, Vincent [VerfasserIn]
• Titel: Tree quantum field theory
• Verf.angabe: Razvan Gurau, Jacques Magnen and Vincent Rivasseau
• E-Jahr: 2009
• Jahr: July 25, 2009
• Umfang: 25 S.
• Fussnoten: Gesehen am 29.09.2022
• Titel Quelle: Enthalten in: Institut Henri PoincaréAnnales Henri Poincaré
• Ort Quelle: Cham (ZG) : Springer International Publishing AG, 2000
• Jahr Quelle: 2009
• Band/Heft Quelle: 10(2009), 5, Seite 867-891
• ISSN Quelle: 1424-0661
• DOI: doi:10.1007/s00023-009-0002-2
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Feynman Amplitude
• Sach-SW: Feynman Graph
• Sach-SW: Feynman Parameter
• Sach-SW: Parametric Representation
• Sach-SW: Ribbon Graph
• K10plus-PPN: 1805335065

Abstract

We propose a new formalism for quantum field theory (QFT) which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e., it computes correlation functions through convergent rather than divergent expansions. It applies both to Fermionic and Bosonic theories. It is compatible with the renormalization group, and it allows to define non-perturbatively differential renormalization group equations. It accommodates any general stable polynomial Lagrangian. It can equally well treat noncommutative models or matrix models such as the Grosse-Wulkenhaar model. Perhaps most importantly it removes the space-time background from its central place in QFT, paving the way for a non-perturbative definition of field theory in non-integer dimension.