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A new class of generally covariant gauge theories is introduced. The only field in addition to the gauge connection is a scalar-density Lagrange multiplier. For the group SO(3,C) SO(3,R) in four dimensions and particular coupling constants, the theory is equivalent to complex Euclidean general relativity, modulo an important degeneracy. The spacetime metric is constructed from the curvature in a solution. A canonical analysis leads directly to Ashtekar's Hamiltonian formalism. The general solution to the four diffeomorphism constraints in the nondegenerate case is given.
Capovilla et al. (Mon,) studied this question.
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