algorithm suggested in [@Cast] that aims at modifying the Dirac scheme and constructing a generator producing correct transformations for all variables. However, this algorithm fails to be applied to an arbitrary parametrization of gravitational variables, so it is not general enough and cannot be considered as a required solution to the problem.

At the same time, the existence of global BRST symmetry enables us to propose another method based upon the Noether theorem and the equivalence of Lagrangian dynamics and Hamilton dynamics in extended phase space. In this section we shall apply it to our spherically symmetric model, however nothing prevent one from applying it to any other gravitational model including the full theory of gravity. The fact that gauge degrees of freedom are treated on the equal footing with other variables allows one to make transformations of variables including gauge ones which have been proved to be canonical in extended phase space [@Shest1] and do not affect the algebra of Poisson brackets. So, the proposed method will work for any reasonable parametrization of gravitational variables.

You can find the proof of BRST symmetry of the Faddeev – Popov effective action for Yang – Mills fields in any book on 