TRAPs, Generalisations of MZVs, Locality and Resurgence for Quantum Field Theories

TL;DR

This thesis explores mathematical structures in quantum field theory, including TRAPs for Feynman rules, generalisations of MZVs, locality structures, and resurgence theory, providing rigorous foundations and open questions.

Contribution

It introduces TRAPs for defining Feynman rules rigorously, generalises MZVs, and advances the theory of locality and resurgence in quantum field theory.

Findings

TRAPs offer a rigorous framework for Feynman rules

Generalised MZVs exhibit new algebraic properties

Resurgence theory yields summability results

Abstract

This thesis presents some mathematical results related to quantum field theory. The first chapter is dedicated to TRAPs and how they could be used to rigorously define Feynman rules. The second introduces generalisations of MZVs and study their properties. The third gives the main results of the theory of locality structures. The fourth and last chapter presents a summability result within the framework of resurgence theory. Each chapter ends with open questions and conjectures on the domain.