A beginner's guide to functional methods in particle physics

TL;DR

This paper provides an accessible introduction to functional methods in particle physics, explaining their theoretical basis, common truncations, and practical application to calculating observable quantities like the glueball spectrum.

Contribution

It offers a comprehensive overview of functional methods and demonstrates their use in particle physics through a detailed example of glueball spectrum calculation.

Findings

Illustrates the use of Dyson-Schwinger equations and other functional methods in particle physics.

Shows how to implement truncations and solution techniques for practical calculations.

Calculates the glueball spectrum as an example of applying these methods.

Abstract

Functional methods like Dyson-Schwinger equations, the nPI effective action formalism, bound state equations and the functional renormalization group are versatile tools to study quantum field theories. They are exact, nonperturbative equations but have to be truncated for practical calculations. After a general introduction, I focus on their use in particle physics and discuss common truncations and solution techniques. The complete process from choosing a truncation to calculating observable quantities is exemplified by means of the glueball spectrum.