Understand
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.