Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme

TL;DR

This paper demonstrates how the BPHZ momentum renormalization scheme, based on Connes-Kreimer Hopf algebra, can be applied to any renormalizable combinatorially non-local field theory, enabling explicit amplitude calculations.

Contribution

It extends the BPHZ momentum scheme to all renormalizable combinatorially non-local field theories using algebraic methods, enhancing understanding and enabling new calculations.

Findings

Applied BPHZ scheme to non-local theories

Provided explicit amplitude calculations in tensorial theories

Improved understanding of noncommutative field theory

Abstract

Various combinatorially non-local field theories are known to be renormalizable. Still, explicit calculations of amplitudes are very rare and restricted to matrix field theory. In this contribution I want to demonstrate how the BPHZ momentum scheme in terms of the Connes-Kreimer Hopf algebra applies to any combinatorially non-local field theory which is renormalizable. This algebraic method improves the understanding of known results in noncommutative field theory in its matrix formulation. Furthermore, I use it to provide new explicit perturbative calculations of amplitudes in tensorial field theories of rank $r>2$.