Canonical quantization of Yang-Mills on a circle

The canonical quantization of YM on a circle in the temporal gauge is developed in two different mathematically rigorous formulations. In the first case the basic coordinates are the gauge potentials and we give a complete construction, but find no observables. In the second case the basic coordinates are the holonomy operators (Wilson loop operators) and here we also give a construction. A key ingredient is a proof that the irreducible characters of the holonomy operators are eigenvectors for the Hamiltonian.