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arXiv · 2212.03502

Three-loop photon spectral density in QED

A. I. Onishchenko
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Abstract

We calculate three-loop photon spectral density in QED with $N$ different species of electrons. The obtained results were expressed in terms of iterated integrals, which are either reduce to Goncharov's polylogarithms or can be written in terms of one-fold integrals of harmonic polylogarithms and complete elliptic integrals. In addition we provide threshold and high-energy asymptotics of the calculated spectral density. It is shown, that the use of the obtained spectral density correctly reproduces separately calculated moments of corresponding photon polarization operator.

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A. I. Onishchenko. 2022-12-07. Three-loop photon spectral density in QED. https://arxiv.org/abs/2212.03502

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