  Quantum gravity effects of zeroth order in the Planck constant are
investigated in the framework of the low-energy effective theory. A special
emphasis is placed on establishing the correspondence between classical and
quantum theories, for which purpose transformation properties of the
\hbar^0-order radiative contributions to the effective gravitational field
under deformations of a reference frame are determined. Using the
Batalin-Vilkovisky formalism it is shown that the one-loop contributions
violate the principle of general covariance, in the sense that the quantities
which are classically invariant under such deformations take generally
different values in different reference frames. In particular, variation of the
scalar curvature under transitions between different reference frames is
calculated explicitly. Furthermore, the long-range properties of the two-point
correlation function of the gravitational field are examined. Using the
Schwinger-Keldysh formalism it is proved that this function is finite in the
coincidence limit outside the region of particle localization. In this limit,
the leading term in the long-range expansion of the correlation function is
calculated explicitly, and the relative value of the root mean square
fluctuation of the Newton potential is found to be 1/\sqrt{2}. It shown also
that in the case of a macroscopic gravitating body, the terms violating general
covariance, and the field fluctuation are both suppressed by a factor 1/N,
where N is the number of particles in the body. This leads naturally to a
macroscopic formulation of the correspondence between classical and quantum
theories of gravitation. As an application of the obtained results, the secular
precession of a test particle orbit in the field of a black hole is determined.
