QUANTUM DIFFEOMORPHISMS AND CONFORMAL SYMMETRY

We analyze the constraints of general coordinate invariance for quantu m theories possessing conformal symmetry in four dimensions. The chara cter of these constraints simplifies enormously on the Einstein univer se RxS(3). The SO(4,2) global conformal symmetry algebra of this space determines uniquely a finite shift in the Hamiltonian constraint from its classical value. In other words, the global Wheeler-De Witt equat ion is modified at the quantum level in a well-defined way in this cas e. We argue that the higher moments of T-00 should not be imposed on t he physical states a priori either, but only the weaker condition [<(T )over dot (00)>] = 0. We present an explicit example of the quantizati on and diffeomorphism constraints on RxS(3) for a free conformal scala r field.