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arXiv · 1004.2202

On the Summation of Feynman Graphs

H. M. Fried·Y. Gabellini
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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.

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H. M. Fried, Y. Gabellini. 2010-04-13. On the Summation of Feynman Graphs. https://doi.org/10.1016/j.aop.2012.03.001

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