Generalized coordinates on the phase space of Yang-Mills theory

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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-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.