Power Counting Rules for Next-to-Leading Order Hard Thermal Loop Theory
The goal of this thesis is to determine power counting rules at next-to-leading order (NLO) in the hard thermal loop (HTL) resummation. The original paper by Braaten and Pisarski discusses NLO HTL resummation and argues that there are potentially three types of contributions. We start by studying these terms in the specific case of the boson and fermion self energies in QED and QCD, as these quantities have been calculated in previous literature. For the real and imaginary parts of the fermion and gluon self energies, one needs to calculate only one type of term, as the other two are found to be subleading. However, for the real and imaginary parts of the photon self energy, all types of terms need to be calculated.