  The conformal factor of the spacetime metric becomes dynamical due to the
trace anomaly of matter fields. Its dynamics is described by an effective
action which we quantize by canonical methods on the Einstein universe $R\times
S^3$. We find an infinite tower of discrete states which satisfy the
constraints of quantum diffeomorphism invariance. These physical states are in
one-to-one correspondence with operators constructed by integrating integer
powers of the Ricci scalar.
