Gauge Theory Without Principal Fiber Bundles

Abstract In general relativity, the strong equivalence principle is underpinned by a geometrical account of fields on spacetime, by which all fields and bodies probe the same geometry. This geometric account implies that the parallel transport of all spacetime tensors and spinors is dictated by a single affine connection. No similar account of gauge theory is put forward by standard textbooks, which use principal bundles to coordinate the parallel transport of different, interacting particles. Nonetheless, here I argue that gauge theory does afford such a geometric account, obviating the need for principal bundles.