Nonequilibrium gauge field in Two Particle Irreducible real time formalism

Abstract: The purpose of this thesis is to study what effect a photon field has on the equations of motion and the decay of a charged scalar field in thermal equilibrium at finite temperature and outside of thermal equilibrium. To do this we calculate the two-particle irreducible effective action for the mean fields and propagators and derive their equations of motion. The functional representations of up to two loop diagrams and their contributions to the self energies of the scalar, photon and mixed propagators and the scalar and photon mean fields have been calculated. We have calculated the one loop correction to the thermal masses of the scalar and photon field and the decay width of the scalar field from these diagrams. The one loop diagram contributing to the decay width is dependent on the internal loop momentum and thus provides an interesting energy and temperature dependence in the width that we have not found in the literature prior to this work. Parallels to semiconductor physics and the dispersion relation of incident light into a semiconductor are drawn to the decay of the scalar field and the energy and temperature dependence of the decay. The temperature dependent contribution to the width could potentially have a great importance in the early universe and the study of the evolution of mean fields when the temperature was high. It could be important for several events that occurred in the early universe, such as phase transitions and entropy generation. We solve the equations of motion numerically using Mathematica and present some plots of the decay for various initial conditions.