Recursive Graphical Construction of Tadpole-Free Feynman Diagrams and Their Weights in phi^4-Theory

TL;DR

This paper reviews methods for generating tadpole-free Feynman diagrams in phi^4-theory, crucial for calculating critical exponents using renormalization in four minus epsilon dimensions.

Contribution

It introduces a recursive graphical construction method for tadpole-free diagrams and discusses their weights, enhancing diagram generation techniques in quantum field theory.

Findings

Developed a recursive method for diagram generation

Clarified the weights of tadpole-free diagrams

Facilitated calculations of critical exponents in phi^4-theory

Abstract

We review different approaches to the graphical generation of the tadpole-free Feynman diagrams of the self-energy and the one-particle irreducible four-point function. These are needed for calculating the critical exponents of the euclidean multicomponent scalar phi^4-theory with renormalization techniques in d=4-epsilon dimensions.