Linearized Quantum Gravity Using the Projection Operator Formalism
  The theory of canonical linearized gravity is quantized using the Projection Operator formalism, in which no gauge or coordinate choices are made. The ADM Hamiltonian is used and the canonical variables and constraints are expanded around a flat background. As a result of the coordinate independence and linear truncation of the perturbation series, the constraint algebra surprisingly becomes partially second-class in both the classical and quantum pictures after all secondary constraints are considered. While new features emerge in the constraint structure, the end result is the same as previously reported: the (separable) physical Hilbert space still only depends on the transverse-traceless degrees of freedom. 
Wayne R. Bomstad and John R. Klauder