  Emergence of fundamental forces from gauge symmetry is among our most
profound insights about the physical universe. In nature, such symmetries
remain hidden in the space of internal degrees of freedom of subatomic
particles. Here we propose a way to realize and study gauge structures in real
space, manifest in external degrees of freedom of quantum states. We present a
model based on a ring-shaped lattice potential, which allows for both Abelian
and non-Abelian constructs. Non trivial Wilson loops are shown possible via
physical motion of the system. The underlying physics is based on the close
analogy of geometric phase with gauge potentials that has been utilized to
create synthetic gauge fields with internal states of ultracold atoms. By
scaling up to an array with spatially varying parameters, a discrete gauge
field can be realized in position space, and its dynamics mapped over
macroscopic size and time scales.
