Research Article Renormalization of QED Near Decoupling Temperature Samina S. Masood Physics Department, University of Houston Clear Lake, Houston, TX 77058, USA Correspondence should be addressed to Samina S. Masood; masood@uhcl.edu Received 26 December 2013; Revised 28 April 2014; Accepted 7 May 2014; Published 24 June 2014 Academic Editor: Ali Hussain Reshak Copyright © 2014 Samina S. Masood. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We study the efective parameters of QED near decoupling temperatures and show that the QED perturbative series is convergent, at temperatures below the decoupling temperature. he renormalization constant of QED acquires diferent values if a system cools down from a hotter system to the electron mass temperature or heats up from a cooler system to the same temperature. At =, the irst order contribution to the electron self-mass, / is 0.0076 for a heating system and 0.0115 for a cooling system and the diference between two values is equal to 1/3 of the low temperature value and 1/2 of the high temperature value around ∼. his diference is a measure of hot fermion background at high temperatures. With the increase in release of more fermions at hotter temperatures, the fermion background contribution dominates and weak interactions have to be incorporated to understand the background efects. 1. Introduction Renormalization techniques of perturbation theory are used to calculate temperature dependence of renormalization constants of QED (quantum electrodynamics) at inite tem- peratures [1–11]. he values of electron mass, charge, and wavefunction, at a given temperature, represent the efective parameters of QED at those temperatures. he magnetic moment of electrons, dynamically generated mass of pho- tons, and QED coupling constants are estimated as functions of temperature. However, thermal contributions to electric permittivity, magnetic permeability, and dielectric constant of the medium are derived from the vacuum polarization. Some of the important parameters of QED plasma such as Debye shielding length, plasma frequency, and the phase transitions can be obtained from the properties of the medium itself. In this paper, we reexamine the analytical results of tem- perature dependent renormalization constants and prove that QED can safely be renormalized at inite temperatures, using the perturbation theory in a vacuum, below the neutrino decoupling temperature. We use the renormalization scheme of QED in real-time formalism [1–8] to calculate the electron mass, wavefunction, and charge of electron as renormaliza- tion constants of QED [9–11]. It is now well known that the existing irst order calculations of the renormalization constants, in the real-time formalism, give the quadratic dependence of QED parameters on temperature , expressed in units of electron mass . Renormalization constants of QED, using the perturbation theory, give efective parameters of QED in a hot and dense medium and are very useful to understand the physics of the universe. However, the renormalization scheme is fully reliable below the decoupling temperature only. It is explicitly checked that, in the existing scheme of calculations, the theory remains renormalizable at ≤4∼2 MeV. However, the perturbative corrections will exceed the original values of QED parameters at higher temperatures and hard thermal loops have to be dealt with, using already developed methods [12–14]. However, below the neutrino decoupling temperature, the real part of the propagators is enough to describe the perturbative behavior of the system and doubling of the ield is not required. We discuss here the distinct behavior of QED below the neutrino decoupling temperatures. At these tempera- tures, QED coupling starts to play its role in modifying QED parameters for nucleosynthesis. With the help of these efective parameters of QED, the abundance of helium in the early universe can be estimated [12] precisely at a given temperature. he temperature dependent QED corrections to the nucleosynthesis parameters improve the results of the Hindawi Publishing Corporation Physics Research International Volume 2014, Article ID 489163, 9 pages http://dx.doi.org/10.1155/2014/489163