  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.
