Three Principles for Quantum Gravity

Abstract

We postulate that the fundamental principles of Quantum Gravity are diffeomorphism symmetry, unitarity, and locality. Local observables are compatible with diffeomorphism symmetry in the presence of diff anomalies, which modify the symmetry algebra upon quantization. We describe the generalization of the Virasoro extension to the diffeomorphism algebra in several dimensions, and its off-shell representations. These anomalies can not arise in QFT, because the Virasoro-like cocycles are functionals of the observer's spacetime trajectory, which is not present in QFT. Possible implications for physics are discussed.