Philosophy of Physics Seminar (Thursday - Week 5, MT25)

Abstract: Symmetries lie at the heart of gauge theory—or so it is said. The familiar, symmetry-first formulation of a gauge theory begins with a Lie group of transformations that constrains the theory's admissible structures, interactions, and observables. In this talk I present an alternative, geometry-first formulation, applicable to a well-defined subset of gauge theories. In this approach, symmetry does not appear at the ground level of explanation and need not be invoked at all. The basic entities are not principal bundles and their connections but 'fundamental' or 'atomic' vector bundles and their covariant derivatives, from which symmetry is recovered—if at all—as a derived notion. I will show that the geometry-first subset excludes many symmetry-first theories but, fortunately, includes the Standard Model. Finally, time permitting, I will illustrate how this perspective clarifies the Higgs and Yukawa mechanisms and reshapes explanations of charge quantisation and mass generation.