Abstract
Various symmetries of elementary particles can be represented by gauge transformations acting on a fiber of the tangent bundle. These are diffeomorphisms of linear groups which act on vertical vector fields. It is shown how the electroweak vector boson potentials and a corresponding Kaluza-Klein-like metric can be obtained by application of SU(2) × U(1) to a tangent fiber. This geometry gives a more unified approach to gravitation and gauge symmetries.
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