Topological tunneling and Goldstone gluons

Canonically quantizing in the temporal gauge $A_0=0$, we study the symmetry properties of the gauge theory vacuum under time-independent gauge transformations. A quantum-electrodynamics-like unconfined phase exhibits spontaneously broken symmetry under gauge transformations that do not vanish at spatial infinity. In a confining phase this symmetry should be restored. When in the unconfined phase, assuming it exists, of a theory possessing topologically nontrivial gauge transformations, the physical Hilbert space will admit a discrete symmetry operation related to a tunneling process between discrete classical vacuums. In the confined phase, this symmetry becomes part of a continuous gauge symmetry. We discuss in detail the solvable theories of free photons and the two-dimensional Schwinger model. We also give some nonrigorous arguments that the phase $\theta$ associated with the tunneling process may have no physical significance in four-dimensional space-time.