The conformal factor of the spacetime metric becomes dynamical due to
the trace anomaly of matter fields. Its dynamics is described by an ef
fective action which we quantize by canonical methods on the Einstein
universe RxS(3). We find an infinite tower of discrete stales which sa
tisfy the constraints or quantum diffeomorphism invariance. These phys
ical states are in one-to-one correspondence with operators constructe
d by integrating integer powers of the Ricci scalar.