Recursive Graphical Construction for Feynman Diagrams of Quantum Electrodynamics

TL;DR

This paper introduces a recursive graphical method for constructing Feynman diagrams in quantum electrodynamics, accurately determining their multiplicities without using external sources, and deriving n-point functions from vacuum energy.

Contribution

The paper presents a novel recursive approach for generating Feynman diagrams and their multiplicities directly from a functional differential equation, avoiding external sources.

Findings

Successfully constructs all vacuum energy diagrams in QED

Derives n-point functions via functional differentiation

Provides a recursive method applicable to complex diagrams

Abstract

We present a method for a recursive graphical construction of Feynman diagrams with their correct multiplicities in quantum electrodynamics. The method is first applied to find all diagrams contributing to the vacuum energy from which all n-point functions are derived by functional differentiation with respect to electron and photon propagators, and to the interaction. Basis for our construction is a functional differential equation obeyed by the vacuum energy when considered as a functional of the free propagators and the interaction. Our method does not employ external sources in contrast to traditional approaches.