Einstein's equations and locality

The problem of formulating a local quantum theory of Einstein equations is examined. It is proved that Einstein equations cannot hold as operator equations if written in terms of a potentialh_µ(D) which is a weakly local field. This result is independent of the kind of metric chosen in the Hilbert space and it doesn't require covariance ofh_µ.As a consequence, the peculiar features of the radiation gauge method, i.e. non locality and non covariance, appear as necessary features of any solution not involving unphysical particles.On leave of absence from: Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Pisa, Italy.