  We study the suitability of complex Wilson loop variables as (generalized)
coordinates on the physical phase space of $SU(2)$-Yang-Mills theory. To this
end, we construct a natural one-to-one map from the physical phase space of the
Yang-Mills theory with compact gauge group $G$ to a subspace of the physical
configuration space of the complex $G^\C$-Yang-Mills theory. Together with a
recent result by Ashtekar and Lewandowski this implies that the complex Wilson
loop variables form a complete set of generalized coordinates on the physical
phase space of $SU(2)$-Yang-Mills theory. They also form a generalized
canonical loop algebra. Implications for both general relativity and gauge
theory are discussed.
