Shane Farnsworth: Rethinking Connes' Approach to the Standard Model of Particle Physics via NCG

The preceding talk described a reformulation of Connes' non-commutative geometry (NCG), and some of its consequences for the NCG construction of the standard model of particle physics. Here we explain how this same reformulation yields a new perspective on the symmetries of a given NCG. Applying this perspective to the NCG traditionally used to describe the standard model we find, instead, an extension of the standard model by an extra U(1)_{B-L} gauge symmetry, and a single extra complex scalar field sigma, which is a singlet under SU(3)_{C} \times SU(2)_{L} \times U(1)_{Y} but has B-L=2. This field has cosmological implications, and offers a new solution to the discrepancy between the observed Higgs mass and the NCG prediction.

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