A Technique for generating Feynman Diagrams

TL;DR

The paper introduces a straightforward bootstrap-based technique to generate Feynman diagrams for various vector models, automating symmetry factors and signs, applicable to high-order calculations and different models including fermionic and gauge theories.

Contribution

It presents a novel bootstrap method for systematically generating Feynman diagrams in vector models using only free field energy values.

Findings

Automatically generates symmetry factors and signs for diagrams.

Applicable to high-order diagrams and various models.

Potential extension to QED as a non-local Thirring model.

Abstract

We present a simple technique that allows to generate Feynman diagrams for vector models with interactions of order $2n$ and similar models (Gross-Neveu, Thirring model), using a bootstrap equation that uses only the free field value of the energy as an input. The method allows to find the diagrams to, in principle, arbitrarily high order and applies to both energy and correlation functions. It automatically generates the correct symmetry factor (as a function of the number of components of the field) and the correct sign for any diagram in the case of fermion loops. We briefly discuss the possibility of treating QED as a Thirring model with non-local interaction.