Abstract
The gauge ‘‘internal’’ symmetriesa which span the Standard Model, in the Physics of Particles and Fields, partly involve a mechanism of Spontaneous Symmetry Breakdown (SSB), whose present formulation (by P. Higgs, T. Kibble, P. Anderson and others) was inspired by phase transition mechanisms in the Physics of Condensed Matter. The role of the order parameter, breaking the internal symmetry, is assumed to be filled by Lorentz‐scalar fields. However, whereas gauge bosons in ordinary gauge theories correspond to connections in Fibre Bundle geometries and thus obey severe algebraic and geometrical constraints, the SSB scalar fields seem arbitrarily ‘‘put in by hand’’. Several suggestions have been made since the Seventies, all aiming at an appropriately constraining geometrization of the scalar fields. In these lectures, I review three such related approaches: (1) internal supersymmetry, (2) the superconnection, (3) non‐commutative geometry.
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