Moments and spectral density of photon polarization function in QED
Submitted: 03.12.2024; Published 13.12.2024 , Updated on 07.03.2025
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Andrei Onishchenko, R. M.  Iakhibbaev. "Moments and spectral density of photon polarization function in QED" Natural Sci. Rev. 1 4 (2024)
https://nsr-t.jinr.ru/index.php/nsr/article/view/22
Andrei Onishchenko1,2,a, R. M.  Iakhibbaev1,b
  • 1Bogoliubov Laboratory of Theoretical Physics
  • 2Sarov Branch of Moscow State University
  • aonish@bk.ru
  • byakibaev@jinr.ru
Natural Sci. Rev. 1 4 (2024) 13.12.2024
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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.