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Superconnections: an interpretation of the standard model. (English) Zbl 0999.81093
Summary: The mathematical framework of superbundles as pioneered by D. Quillen suggests that one considers the Higgs field as a natural constituent of a superconnection. I propose to take as superbundle the exterior algebra obtained from a Hermitian vector bundle of rank \(n\) where \(n=2\) for the electroweak theory and \(n=5\) for the full Standard Model. The present setup is similar to but avoids the use of noncommutative geometry.

MSC:
81V22 Unified quantum theories
53C80 Applications of global differential geometry to the sciences
58A50 Supermanifolds and graded manifolds
81R40 Symmetry breaking in quantum theory
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