Abstract
In this PhD-thesis some topics in quantum field theory are considered. The first chapter gives a background to these topics. The second chapter discusses renormalization. In particular it is shown how loop calculations can be performed when using the axial gauge fixing. Fermion creation and annihilation configurations for the one loop level are obtained and an example calculations was done to check that these lead to gauge invariant amplitudes. The next topic in the second chapter is renormalization prescriptions. The scheme-dependence that these prescriptions lead to is discussed and we come up with a re-expanded perturbative series that turns the scheme-dependent series into a scheme-independent one. We check that numerical results are similar to the ones obtained from some often-used renormalization presecriptions. The third chapter considers the electroweak standard model in the axial gauge. The Feynman rules are derived and particle creation and annihilation configurations are defined. Using these two ingredients it is, in principle, possible to do tree-level calculations. The fourth chapter is concerned with unstable particles. The problem that cross sections diverge when the colliding particles are unstable is discussed. We derive that an effective cross section that is proportional to the size of the incoming wave packets can be defined. This is the linear beam size effect. This derivation is done in a manifestly Lorentz invariant manner. Furthermore, a Monte Carlo prescription is given that incorporates this effect into the usual integration procedure. This chapter also goes into the case of incoming wave packets that are very large. A very strange prescription, involving complex momentum components, was proposed in the literature. We replace this prescription by a more reasonable one. We also consider the case where the incoming unstable particle is in a pancake-shaped wave packet.
