GEOMETRICAL REPRESENTATION OF EUCLIDEAN GENERAL-RELATIVITY IN THE CANONICAL FORMALISM

We give an SU(2) covariant representation of the constraints of Euclid ean general relativity in the Ashtekar variables. The guiding principl e is the use of triads to transform all free spatial indices into SII (2) indices. A central role is played by a special covariant derivativ e. The Gauss, diffeomorphism and Hamiltonian constraints become purely algebraic restrictions on the curvature and the torsion associated wi th this connection. We introduce coordinates on the jet space of the d ynamical fields, which cleanly separate the constraint and gauge direc tions from the true physical directions. This leads to a classificatio n of all local diffeomorphism and Gauss invariant charges.