PhD thesis Defense:
"Renormalization of SU(2) Yang-Mills theory with flow equations"
Wednesday, September 27th at 3:00pm, Room conference, CPHT, Building 6
Abstract: The problem of perturbative renormalization of SU(2) Yang-Mills theory is studied in four dimensional Euclidean space with Lorenz gauge fixing. The analysis is based on the renormalization group flow equations. This is a unified approach which permits to study a large class of field theories without recourse to Feynman diagrams. It is remarkable that the flow equations allow us to construct all vertex functions of the theory using only the renormalization conditions. An important part of the work consists in establishing upper bounds in momentum space on all vertex functions at all loop orders. These bounds have a very natural graphical interpretation in form of trees. In order to properly define the vertex functions one must introduce ultraviolet and infrared cut-offs. But this regularization breaks BRST invariance. Thus it is essential to prove at all loop orders that the construction can be accomplished in such a way that BRST invariance is restored when the UV cut-off goes to infinity. Furthermore, substantial effort is made to provide a physical renormalization scheme which is explicitly independent of the flow parameter.