How I Learned to Stop Worrying and Love QFT

TL;DR

This paper provides a mathematically rigorous perspective on quantum field theory, explaining how to interpret perturbative expansions and Feynman integrals using distribution theory to address convergence and divergence issues.

Contribution

It introduces a framework that clarifies the mathematical foundations of QFT, emphasizing the use of distributions over divergent integrals, which is a novel approach in the field.

Findings

Perturbative expansions can be made sense of through distribution theory.

Feynman loop integrals and renormalization are expressed rigorously using distributions.

QFT can be better understood mathematically than traditional introductions suggest.

Abstract

Lecture notes of a block course explaining why quantum field theory might be in a better mathematical state than one gets the impression from the typical introduction to the topic. It is explained how to make sense of a perturbative expansion that fails to converge and how to express Feynman loop integrals and their renormalization using the language of distribtions rather than divergent, ill-defined integrals.