  It is possible to find different sets of local coordinates in the field space
of Yang-Mills theories which implement Gauss' law manifestly for physical
states. The singular points of the transformations to these gauge-invariant
coordinates induce energy barriers in the Hamiltonian much like angular
momentum in quantum mechanics, and these formulations suggest a vacuum state
functional qualitatively different from the perturbative one. Lecture given at
the XIII Particles and Nuclei International Conference, Perugia, Italy, June 28
- July 2, 1993.
