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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.