The pure Yang-Mills field, I: fixed time existence

The convergence of renormalized perturbation theory to all finite orders is defined and shown to be valid for the fixed time perturbation theory of a pure Yang-Mills field. Two pure Yang-Mills quantum gauge field theories are constructed, one based on short distance asymptotics and the other based on long distance asymptotics. The construction depends on an assumed principle of a maximum rate of entropy production.