GENERALIZED COORDINATES ON THE PHASE-SPACE OF YANG-MILLS THEORY

We study the suitability of complex Wilson loop variables as (generali zed) coordinates on the physical phase space of SU(2) Yang-Mills theor y. To this end, we construct a natural one-to-one map from the physica l 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 Lewandows ki this implies that the complex Wilson loop variables form a complete set of generalized coordinates on the physical phase space of SU(2) Y ang-Mills theory. They also form a generalized canonical loop algebra. Implications for both general relativity and gauge theory are discuss ed.