We continue the study of physical fields for the background free 4D quantum
gravity based on the Riegert-Wess-Zumino action, developed in Phys. Rev. D {\bf
85} (2012) 024028. The background free model is formulated in terms of a
certain conformal field theory on M^4 in which conformal symmetry arises as
gauge symmetry, namely diffeomorphism invariance. In this paper, we construct
the physical field operator corresponding to any integer power of Ricci scalar
curvature in the context of the BRST quantization. We also discuss how to
define the correlation function and its physical meanings.Comment: 22 pages, minor typo corrected, published versio
