Mode d'emploi de la th\'eorie constructive des champs bosoniques (A user's guide to bosonic constructive field theory)

TL;DR

This paper provides a comprehensive guide to the constructive methods used in bosonic quantum field theory, aiming to make these techniques rigorous for mathematicians and mathematical physicists.

Contribution

It offers a detailed, accessible presentation of the principal constructive arguments specifically for bosonic theories, filling a gap in recent literature.

Findings

Clarifies the constructive framework for bosonic quantum field theories

Bridges quantum field theory and rough path theory

Provides rigorous mathematical foundations for bosonic models

Abstract

We develop in this article the principal constructive arguments used in quantum field theory, limiting us to bosonic theories, for which there does not exist any recent general presentation. The article is primarily written for mathematicians or mathematical physicists knowing the basic arguments of quantum field theory, and desiring to discover a general framework in which they can be made rigorous. It also provides a glimpse of a recent series of articles \cite{MagUnt1,MagUnt2} whose aim is to give a constructive definition of rough paths and fractionary stochastic calculus.