Work

Perturbative renormalisation of the $\Phi^{4}_{4-\varepsilon}$ model via generalised Wick maps

Year: 2026

Type: article

Abstract: We consider the perturbative renormalisation of the \Phi^{4}_{d} model from Euclidean quantum field theory for any possibly non-integer dimension d<4 . The so-called BPHZ renormalisation, named after Bogoliubov, Parasiuk, Hepp, and Zimmermann, is usually encoded into extraction-contraction operations on Feynman diagrams, which have a complicated combinatorics. We show that the same procedure can be encoded in the much simpler algebra of polynomials in two unknowns X and Y , which represent the fourth and second Wick power of the field. In this setting, renormalisation takes the form of a “Wick map” that maps monomials into Bell polynomials. The construction makes use of recent results by Bruned and Hou on multi-indices, which are algebraic objects of intermediate complexity between Feynman diagrams and polynomials.

Source: Annales de l’Institut Henri Poincaré D Combinatorics Physics and their Interactions

DOI: 10.4171/aihpd/238

Authors: Nils Berglund, Tom Klose, Nikolas Tapia

Institutions: Université de Tours, Université d'Orléans, Centre National de la Recherche Scientifique, Institut Denis Poisson, University of Oxford, Humboldt-Universität zu Berlin, Weierstrass Institute for Applied Analysis and Stochastics

Language: English

Topic: p-Adic Analysis and Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4414855144

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