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We perform a manifestly covariant quantization of a Weyl invariant, i.e., alocally scale invariant, scalar-tensor gravity in the extended de Donder gaugecondition (or harmonic gauge condition) for general coordinate invariance and anew scalar gauge for Weyl invariance within the framework of BRST formalism. Itis shown that choral symmetry, which is a Poincar${\rm{\acute{e}}}$-like$\IOSp(8|8)$ supersymmetry in case of Einstein gravity, is extended to aPoincar${\rm{\acute{e}}}$-like $\IOSp(10|10)$ supersymmetry. We point out thatthere is a gravitational conformal symmetry in quantum gravity and account forhow conventional conformal symmetry in a flat Minkowski space-time is relatedto the gravitational conformal symmetry. Moreover, we examine the mechanism ofspontaneous symmetry breakdown of the choral symmetry, and show that thegravitational conformal symmetry is spontaneously broken to the Poincar\'esymmetry and the corresponding massless Nambu-Goldstone bosons are the gravitonand the dilaton. We also prove the unitarity of the physical S-matrix on thebasis of the BRST quartet mechanism.

Quantum Theory of Weyl Invariant Scalar-tensor Gravity