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UBC Theses and Dissertations

Perturbative finite temperature field theory in Minkowski space Keil, Werner H.


This thesis contains a perturbative analysis of decay and scattering rates in finite temperature and density environments. The discussion is based on the Niemi-Semenoff real-time formulation of quantum field theory at finite temperature. Two systems are investigated: neutron β decay at finite density, and Higgs boson decay with radiative QED corrections, at finite temperature. For neutron β decay, a fully relativistic analysis at tree level is presented. An analytic formula for the free neutron decay rate is derived, and subsequently generalized to a finite-density environment. The decay rates are obtained from the imaginary part of the neutron self-energy. This method turns out to be very straightforward and elegant, since it includes all relevant decay and inverse decay modes in a nontrivial way. The decay of a Higgs boson into two fermions, with one-loop QED 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, and it is argued that finite-temperature renormalization is not an appropriate concept for decay and scattering rate calculations. 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 on the subject is compared to this general approach, and possible applications in cosmology and astrophysics are discussed.

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