a transition from metric tensor components to the Arnowitt – Deser – Misner (ADM) variables [@ADM], quite legitime in the Lagrangian formulation, should be considered as non-canonical [@KK]. In this case the theory turns out to be essentially dependent on a chosen parametrization.

In the framework of the canonical scheme it is not obvious that the original (Lagrangian) formulation of General Relativity and its Hamiltonian dynamics à la Dirac are theories with different groups of transformations. It has become more clear in the Batalin – Fradkin – Vilkovisky (BFV) approach [@BFV1; @BFV2; @BFV3], that aims at reproducing the Dirac results on the path integral level. A Hamiltonian form of the effective action in this approach is determined by algebra of constraints. The algebra of constraints in the case of gravity is open and, as was emphasized in [@BFV1], gauge transformations differ from transformations generated by gravitational constraints. It may lead to a new type of additional Feynman diagrams corresponding to four-ghosts interaction which cannot result from the effective action in the Lagrangian form. The new type of diagram does not play an important role while one is interested in only gauge invariant sector in the $S$-matrix theory, for which the 