Generalized coordinates on the phase space of Yang-Mills theory

Details Generalized coordinates on the phase space of Yang-Mills theory Generalized coordinates on the phase space of Yang-Mills theory

1994-04-28

arxiv.org/abs/gr-qc/9404060v2

Class.Quant.Grav.12:1191-1198,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

TeX, 11pp, revised version (minor clarifications added, Comment after (2.9) inserted); to appear in Class. Quant. Grav.

Scientific paper

10.1088/0264-9381/12/5/010

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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