Hi folks. I am a mathematician and my research is on the curvature equation D(\gamma) = F where \gamma is a Lie-algebra valued one-form and F is a Lie-algebra-valued 2-form. I want a very rough idea how fiber bundles and associated vector bundles are used in physics. I've tried to read up on it, but most of the stuff is too technical and I just want sort of a bird's eye view of how they are used. More specifically, I'd like to know if you guys ever look at vector bundles whose structure group is Nilpotent. The problem I am working on is when the base manifold is dimension 3 and the structure group is nilpotent.