  Conformal algebra on R x S^3 derived from quantized gravitational fields is
examined. The model we study is a renormalizable quantum theory of gravity in
four dimensions described by a combined system of the Weyl action for the
traceless tensor mode and the induced Wess-Zumino action managing
non-perturbative dynamics of the conformal factor in the metric field. It is
shown that the residual diffeomorphism invariance in the radiation^+ gauge is
equal to the conformal symmetry, and the conformal transformation preserving
the gauge-fixing condition that forms a closed algebra quantum mechanically is
given by a combination of naive conformal transformation and a certain
field-dependent gauge transformation. The unitarity issue of gravity is
discussed in the context of conformal field theory. We construct physical
states by solving the conformal invariance condition and calculate their
scaling dimensions. It is shown that the conformal symmetry mixes the
positive-metric and the negative-metric modes and thus the negative-metric mode
does not appear independently as a gauge invariant state at all.
