A Palatini-type formulation of gravity coupled to matter and supergravity is given, in which the gravitational variables are a trio of self-dual 2-forms and an SL(2,C) connection. The action is polynomial in all the fields. This framework is shown to be the natural covariantization of Ashtekar's canonical formalism (1988), and is used to find the general vacuum solution of the four initial value constraints associated with spacetime diffeomorphisms in that formalism.

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A new action principle, in which the only gravitational variables are an SL(2,C) connection and a scalar density, is derived for general relativity (GR) coupled to matter and for supergravity. In this form, GR appears as a non-metric, generally covariant gauge theory, the metric being reconstructed from the other fields in a solution. A similar non-metric action with a real SO(3,1) connection is also derived, however it involves an independent fourth rank tensor field representing the curvature.

Self-dual solutions to the complex Einstein equation with cosmological constant are characterised as SL(2, C) gauge fields satisfying an equation quadratic in the curvature. For a solution, a tetrad is constructed with respect to which the connection is the left handed spin connection. For real Euclidean signature, the connection reduces to an SU(2) connection.

We carry out the Hamiltonian quantization of a member of a class of' gauge theories in which the internal metric becomes an independent degree of freedom and the gauge group is generalized to SL( N , C ) . The Hamiltonian quantization is carried out both in a gauge where only the SU(,V) synimetry is manifest and in a gauge-invariant way. These theories have been proposed by Cahill, and they also arise as the nongravitational sector of a unified theory of gravitational and gauge fields which has been proposed by one of us (J.D.). The physical degrees of freedom are identified and a relativistically invariant functional generator is constructed. The resulting quantum theory is stable, but not perturbatively renormalizable.