Covariant infrared finite amplitudes

The calculation of observables in gauge theories with massless particles such as QCD - by traditional methods is significantly complicated by the presence of soft and collinear singularities, collectively termed infrared divergences, in the scattering amplitudes. The aim of this thesis is to investigate calculational methods which produce finite results at the amplitude level. We discuss the origin of the infrared divergences and outline some previous approaches to constructing finite amplitudes. After reviewing the traditional method for performing calculations we see how incorrect assumptions result in the presence of infrared divergences and what steps must be taken in order to produce infrared finite results. We then investigate how these ideas could be applied to the calculation of specific amplitudes. We see that there are problems involved in applying this exact approach, but that it suggests the adoption of a workable, more pragmatic alternative. We use this method in an explicit example calculation of the contributing cross sections for the process e+e (^_)> jets at O(as). We demonstrate that we recover the same result as that obtained with standard field theory techniques. We then briefly discuss how this approach might be adapted to suit more complex calculations and, eventually, a completely numerical approach.