On the Summation of Feynman Graphs
High Energy Physics - Theory
2015-05-18 v2
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.
Cite
@article{arxiv.1004.2202,
title = {On the Summation of Feynman Graphs},
author = {H. M. Fried and Y. Gabellini},
journal= {arXiv preprint arXiv:1004.2202},
year = {2015}
}