Tadpole Summation by Dyson-Schwinger Equations

TL;DR

This paper presents a method using Dyson-Schwinger equations to sum tadpole and snail diagrams in quantum field theory, simplifying perturbative calculations by effectively modifying parameters.

Contribution

It introduces a novel approach to sum momentum-independent subdiagrams in perturbation theory through Dyson-Schwinger equations, reducing diagram complexity.

Findings

Significantly reduces the number of diagrams in perturbative expansions

Provides a systematic way to sum tadpole and snail diagrams

Facilitates higher-order perturbative calculations

Abstract

In quantum field theory with three-point and four-point couplings the Feynman diagrams of perturbation theory contain momentum independent subdiagrams, the ``tadpoles'' and ``snails''. With the help of Dyson-Schwinger equations we show how these can be summed up completely by a suitable modification of the mass and coupling parameters. This reduces the number of diagrams significantly. The method is useful for the organisation of perturbative calculations in higher orders.