Abstract:

Abstract: Connes and others have developed a notion of non-commutative geometry (NCG) that generalizes Riemannian geometry, and provides a framework in which the standard model of particle physics, coupled to Einstein gravity, may be concisely and elegantly recast. I will explain how this formalism may be reformulated in a way that naturally generalizes from non-commutative to non-associative geometry. In the process, several of the standard axioms of NCG are conceptually reinterpreted. This reformulation also suggests a new constraint on the class of NCGs used to describe the standard model of particle physics. Remarkably, this new condition resolves a long-standing puzzle about the embedding of the standard model in NCG, by precisely eliminating from the action formula the collection of seven unwanted terms that previously had to be removed by an extra (empirically-motivated, ad hoc) assumption.