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For weak and strong forces, the picture of the potential as a connection on a principal bundle whose curvature is the field strength makes a great deal of sense but the ‘original’ gauge theory for electromagnetism is probably not right.  There is something more subtle going on with electromagnetism — the ‘circles’ of the circle bundle lie in the S4(1/h) universe and intersect each other depending on the extrinsic geometry of the physical universe.  In particular we are not quite dealing with a principal $U(1)$-bundle.  The intersections of these normal circles presumably have an effect on all aspects of electromagnetism.  We don’t really have a local $U(1)$-gauge invariance.