Conformally Coupled General Relativity

Gravity model developed in the series of papers \cite{Arbuzov:2009zza,Arbuzov:2010fz,Pervushin:2011gz} is revisited. Model is based on Ogievetsky theorem that specifies structure of general coordinate transformation group. The theorem is implemented in the context of Noether theorem with the use of nonlinear representation technique. Canonical quantization is performed with the use of reparametrization-invariant time and ADM foliation techniques. Basic quantum features of the models are discussed. Mistakes occurred in the previous papers are corrected.