A Primer on Functional Methods and the Schwinger-Dyson Equations

TL;DR

This paper provides an accessible introduction to functional methods and Schwinger-Dyson equations, focusing on practical techniques like diagrammatic generation, renormalization, and solution methods for advanced applications.

Contribution

It offers new practical insights and methods for generating and solving Schwinger-Dyson equations, which are not typically covered in standard textbooks.

Findings

Develops a diagrammatic method for high-order equations

Explores different forms of Schwinger-Dyson equations

Discusses renormalization and solution techniques

Abstract

An elementary introduction to functional methods and the Schwinger-Dyson equations is presented. Emphasis is placed on practical topics not normally covered in textbooks, such as a diagrammatic method for generating equations at high order, different forms of Schwinger-Dyson equations, renormalisation, and methods for solving Schwinger-Dyson equations.