Existence of Asymptotic Expansions in Noncommutative Quantum Field Theories

TL;DR

This paper investigates the asymptotic behavior of Feynman amplitudes in noncommutative scalar quantum field theories using Mellin representations, providing a comprehensive analysis of scaling properties for various subsets of external invariants.

Contribution

It extends the Mellin representation approach to analyze asymptotic expansions in noncommutative quantum field theories, including both convergent and renormalized amplitudes.

Findings

Established the existence of asymptotic expansions for noncommutative Feynman amplitudes.

Generalized the analysis to arbitrary subsets of external invariants.

Applied the framework to both convergent and renormalized cases.

Abstract

Starting from the complete Mellin representation of Feynman amplitudes for noncommutative vulcanized scalar quantum field theory, introduced in a previous publication, we generalize to this theory the study of asymptotic behaviours under scaling of arbitrary subsets of external invariants of any Feynman amplitude. This is accomplished for both convergent and renormalized amplitudes.