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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.

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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