Quantization of Einstein's Gravitational Field: General Treatment

Abstract

The quantization of the complete gravitational field is carried out by extending the work of an earlier paper. The main obstacles in the quantization of Einstein's field are overcome by expressing the field quantities in the Riemannian space as expansions in the flat space, and then splitting the gravitational field into the linear and the non-linear parts. The linear part of the gravitational field is regarded as the free gravitational field, while the non-linearity is treated as a direct interaction between the gravitons. This treatment is quite general, but it suffers from the usual limitations of the perturbation method. The gravitational self-energies of the photon and the electron are also investigated by using the linear approximation of the gravitational field It is found that the photon self-energy vanishes unambiguously, while the electron self-energy is quadratically divergent.