  It has been observed in [Park 2014] that the physical states of the ADM
formulation of 4D Einstein gravity holographically reduce and can be described
by a 3D language. Obviously the approach poses the 4D covariance issue; it
turns out that there are two covariance issues whose address is the main theme
of the present work. Although the unphysical character of the trace piece of
the fluctuation metric has been long known, it has not been taken care of in a
manner suitable for the Feynman diagram computations; a proper handling of the
trace piece through gauge-fixing is the key to more subtler of the covariance
issues. As for the second covariance issue, a renormalization program can be
carried out covariantly to any loop order at intermediate steps, thereby
maintaining the 4D covariance; it is only at the final stage that one should
consider the 3D physical external states. With the physical external states,
the 1PI effective action reduces to 3D and renormalizability is restored just
as in the entirely-3D approach of [Park 2014]. We revisit the one-loop
two-point renormalization with careful attention to the trace piece of the
fluctuation metric and in particular outline one-loop renormalization of the
Newton's constant.
