Gauge theories are often thought to pose an interpretive puzzle. On the one hand, it seems that some of the mathematical structure of a gauge theory is surplus - that is, it does not reflect any structure in the world. Interpreting this structure as surplus is meant to be especially important to the process of quantization. On the other hand, it has proven difficult to eliminate this putatively surplus structure without losing important features of the theory like empirical adequacy. In this paper I argue that this puzzle is ill-posed, because there is no notion of "surplus structure" on which gauge theories have it. The standard conception of surplus structure presumes an account of mathematical structure that excludes the mathematics of gauge theory, so gauge theories neither have nor lack surplus structure on this conception. And on analyses of "surplus structure" that do apply to gauge theories it's easy to see that they don't have it.
Philosophy of Physics Seminar Convenors for HT20: Oliver Pooley