Introduction to Feynman Integrals

TL;DR

This paper provides an introductory overview of Feynman integrals, covering their role in quantum field theory, mathematical properties, and computational techniques for evaluation.

Contribution

It offers a comprehensive introduction combining foundational concepts, advanced mathematical structures, and practical algorithms for Feynman integrals in quantum field theory.

Findings

Explains perturbative expansion in quantum field theories

Discusses mathematical structures like polylogarithms and shuffle algebras

Reviews algorithms for evaluating Feynman integrals

Abstract

In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced topics: Mathematical aspects of loop integrals related to periods, shuffle algebras and multiple polylogarithms are covered as well as practical algorithms for evaluating Feynman integrals.