Second order thermal corrections to electron wavefunction

Second order perturbative corrections to electron wavefunction are calculated here, for the first time, at generalized temperature. Calculations of electron self energy are important for the renormalizability of electron mass and wavefunction in QED through order by order cancellation of singularities up to order α2. Cancellation of temperature dependent singularities is demonstrated by incorporating the results of both orders of integration between cold and hot loops. For finite terms, we have rewritten second order thermal corrections as well, in a concise form, to calculate wavefunction renormalization constant. Our results are in a form that includes intermediate temperatures T∼m (where m is electron mass) while limits of high temperature T≫m and low temperature T≪m are also retrievable from them. A comparison with the existing results is included as well. The renormalized mass and wavefunction are used to calculate particle processes in extremely hot systems such as stellar cores and primordial nucleosynthesis during very early universe. An application to the latter case is also discussed.