📝 SummarXiv

Abstract

The standard model of particle physics is usually cast in symmetry-first terms. Recently, a geometry-first picture has been proposed, in which the relevant symmetries do not appear explicitly at the ground level of ontology. In this paper I extend this approach to two central mechanisms of the standard model: spontaneous symmetry breaking and the Yukawa coupling, both essential for particles to acquire mass. These reformulations offer alternative explanations cast in purely geometric terms. For example, a particle's quantum numbers correspond to the internal space it inhabits and to the geometric type of object it is (e.g. an $(n,m)$-tensor). I argue that a symmetry-first account in terms of principal and associated bundles admits a genuine geometry-first counterpart only when the group's representation coincides with the automorphism group of the fibre -- a condition that cuts the slack tolerated by the symmetry-first view.