Gauge Fields: What Isn't There?
Richard Healey
Department of Philosophy
University of Arizona

Abstract: A classical Yang-Mills gauge field with symmetry group G (=U(1), SU(2), etc.) may be represented by means of the connection and curvature of a principal fiber bundle P(M,G) whose base space M represents a space-time manifold and whose structure group is G. The empirical success of a theory incorporating such a gauge field interacting with quantum mechanical particles would warrant belief in holistic features of space-time loops. It would not warrant belief in localized features of space-time points, including gauge field strengths or their components at those points. A "sophisticated substantivalist" can defend belief in space-time points and loops against the "hole argument". But an analogous defense of localized gauge features of such points fails.