The Geometry of the "Gauge Argument"

Abstract

We show how the "gauge argument", widely criticized by philosophers as ad hoc and unconvincing, may be reconstructed rigorously, and, we believe, convincingly, as an argument concerning the geometry of vector bundles. In this form, the gauge argument has two parts, the first of which is strongly analogous to the Weyl-Stein argument for Galilean spacetime as the appropriate setting for Newtonian gravitation; and the second of which invokes a classic result in the Yang-Mills theory literature, due to Utiyama [1956, "Invariant Theoretical Interpretation of Interaction", Phys. Rev. 101, 1597].