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Generalized coordinates on the phase space of Yang-Mills theory

R. Loll·J. M. Mourao·J. N. Tavares
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Abstract

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.

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R. Loll, J. M. Mourao, J. N. Tavares. 1995-03-28. Generalized coordinates on the phase space of Yang-Mills theory. https://doi.org/10.1088/0264-9381%2F12%2F5%2F010

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