Calculation of multiple Bremsstrahlung in gauge theories

The method of calculating cross-sections for complex processes in gauge theories at the ultrarelativistic regime, based on a co-variant description of the polarization vectors of the bosons, and on spinors that are eigenvectors of the chirality for the massless fermions, is reviewed. It is then pointed out that there is no need to perform the analysis at the spinorial level, and that trace methods are more efficient. Simpler forms for the polarization vectors are introduced, and a technique to apply these ideas to diagrams involving several fermion lines is developed, all at the trace level. A few representative diagrams are calculated by this technique. A physical interpretation is given as to why some of the poles due to the propagators are single or double order. In the conclusion the present-day situation is studied