  In the present article we display a new constructive quantum field theory
approach to quantum gauge field theory, utilizing the recent progress in the
integration theory on the moduli space of generalized connections modulo gauge
transformations. That is, we propose a new set of Osterwalder Schrader like
axioms for the characteristic functional of a measure on the space of
generalized connections modulo gauge transformations rather than for the
associated Schwinger distributions. We show non-triviality of our axioms by
demonstrating that they are satisfied for two-dimensional Yang-Mills theory on
the plane and the cylinder. As a side result we derive a closed and analytical
expression for the vacuum expectation value of an arbitrary product of Wilson
loop functionals from which we derive the quantum theory along the Glimm and
Jaffe algorithm which agrees exactly with the one as obtained by canonical
methods.
