Pertubative finite temperature field theory in Minkowski space

A perturbative analysis is presented of decay and scattering rates in finite temperature and density environments, based on the Niemi-Semenoff real-time formulation of quantum field theory at finite temperature. Two systems are investigated: neutron beta decay and Higgs boson decay. For neutron beta decay, a fully relativistic analysis at tree level is given. An analytic formula for the free neutron decay rate is derived and generalized to a finite density environment. The decay rates are obtained from the imaginary part of the neutron self-energy (the two-point function of Green's function). This method includes all relevant decay and inverse decay modes in a nontrivial way. The decay of a Higgs boson into two fermions, with one-loop quantum electrodynamic corrections, is used to discuss the problem of renormalization at finite temperature. It is found that the finite temperature part of the self-energy corrections cannot be absorbed into temperature dependent mass and wave function renormalization counterterms due to the lack of Lorentz invariance. A general algorithm for the calculation of thermal self-energy corrections is derived and applied to the Higgs-fermion system. The result is explicitly shown to be free of infrared and mass singularities. Previous work is compared to this general approach, and possible applications in cosmology and astrophysics are discussed.