An Intrinsic Coordinate System Procedure. I. Canonical Weyl Scalars

Canonical quantization of gravity in general relativity is greatly simplified by the artificial decomposition of space and time into a 3+1 formalism. Such a simplification comes at the cost of general covariance. This requires tangential and perpendicular infinitesimal diffeomorphisms generated by the symmetry group under the Legendre transformation of the given action. This gauge generator, along with the fact that Weyl curvature scalars may act as intrinsic coordinates which depend only on the spatial metric g_ab and the conjugate momenta p^cd, allow for an alternative approach to canonical quantization of gravity. In this presentation we present the tensorial solution of the set of Weyl scalars as well as make corrections to the existing literature.