On the Summation of Feynman Graphs

TL;DR

This paper introduces a functional method for summing all relevant Feynman graphs in a given field theory process, applied to QED, leading to gauge-invariant calculations and insights into divergence cancellations and the fine structure constant.

Contribution

It proposes a novel functional approach to sum Feynman graphs, enabling gauge-invariant calculations and divergence analysis in QED.

Findings

Achieved gauge-invariant summation of Feynman graphs in QED.

Extracted leading logarithmic divergences at all perturbative orders.

Demonstrated potential cancellation of divergences affecting the photon wavefunction renormalization.

Abstract

A functional method to achieve the summation of all Feynman graphs relevant to a particular Field Theory process is suggested, and applied to QED, demonstrating manifestly gauge invariant calculations of the dressed photon propagator in approximations of increas- ing complexity. These lead in a natural way to the extraction of the leading logarithmic divergences of every perturbative order, and to a demonstration of the possible cancellation of all such divergences in the calculation of the (inverse of the) photon's wavefunction renormalization constant Z3. This analysis provides a qualitative understanding of why the measured value of the renormalized fine structure constant is, approximately, 1/137.