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Electroweak symmetry on the tangent bundle. (English) Zbl 0979.81093

Summary: 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 \(SU(2) \times U(1)\) to a tangent fiber. This geometry gives a more unified approach to gravitation and gauge symmetries.

MSC:

81V15 Weak interaction in quantum theory
81V22 Unified quantum theories
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
53C80 Applications of global differential geometry to the sciences
81T13 Yang-Mills and other gauge theories in quantum field theory
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