L. Boyle: Non-commutative geometry, non-associative geometry, and the std. model of particle physics

Connes' notion of non-commutative geometry (NCG) generalizes Riemannian geometry and yields a striking reinterepretation of the standard model of particle physics, coupled to Einstein gravity. We suggest a simple reformulation with two key mathematical advantages: (i) it unifies many of the traditional NCG axioms into a single one; and (ii) it immediately generalizes from non-commutative to non-associative geometry. Remarkably, it also resolves a long-standing problem plaguing the NCG construction of the standard model, by precisely eliminating from the action the collection of 7 unwanted terms that previously had to be removed by an extra, non-geometric, assumption. With this problem solved, the NCG algorithm for constructing the standard model action is significantly tighter and more explanatory than the traditional one based on effective field theory.

The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. (23.09.2014)