A polynomial approach to gravitational theories

It is emphasized that, in a classical theory, invariant under general co-ordinate transformations, the nonpolynomial dependence can be reabsorbed by a suitable fields rescaling, if the theory is scale invariant. The new fields show, in the dilatation limit, the canonical UV dimensions. It is derived the BRS differential operator of the new theory and here the results obtained by us in its quantum extensions are shown. The proofs will be given in forthcoming more technical papers