Faddeev Popov Ghosts

These notes are to accompany my talk on gauge xing in quantum eld theories (QFTs), and the mathematical tricks associated with this procedure. In Section 1 I will look at gauge xing for Abelian elds, considering the speci c case of the Maxwell theory describing photons. In Section 2 I consider a non-Abelian generalization of the Maxwell theory called Yang Mills theory, which describes vector bosons or gluons. I demonstrate the necessity of introducing `ghost' elds in order to x the gauge. In Section 3 I look at how ghosts arise as a natural consequence of the geometry of QFTs.