Reference on quantization of linearized gravity I often see claims saying that quantization of linearized gravity can be done. Is there some standard references for it? such as original papers/ review papers / textbooks etc.
 A: The classic papers that started the field are these three from 1967 by Bryce DeWitt:
B. DeWitt, Quantum Theory of Gravity. I, Physical Review, 160:1113–1148, 1967.
B. DeWitt, Quantum Theory of Gravity. II. The Manifestly Covariant Theory, Physical Review, 162:1195–1239, 1967.
B. DeWitt, Quantum Theory of Gravity. III. Application of the Covariant Theory, Physical Review, 162:1239–1256, 1967.
The third paper discusses a variety of interesting calculations, including the cross sections for gravitational scattering of two scalar particles, the scattering of gravitons by scalar particles, graviton-graviton scattering, two-graviton annihilation of scalar-particle pairs, and graviton bremsstrahlung.
In the manifestly covariant approach, the calculations are Feynman-diagram-style, with a propagator for gravitons and vertex rules for how gravitons interact with scalars and with themselves. It looks like QED except with a lot more indices and a lot more terms, but no gamma matrices because he’s using scalars instead of fermions for the “matter”.
The algebra for even these tree-level calculations is onerous and he omits the details. It probably took him months if he did it by hand. Today one would let a computer algebra system crank through it in less than a second.
As you probably know, this approach to quantum gravity is non-renormalizable and therefore not of interest as a “real” theory. But it should be fine at low energies.
