In the last years a lot of papers were published treating general relativity as an effective field theory. We are dealing with general relativity and the combination of general relativity and scalar QED as effective field theories. For effective field theories the quantization is well known therefore we are able to quantize general relativity and the combination of general relativity and scalar QED. The vertex rules can be extracted from the action and the non- analytical contributions to the 1-loop scattering matrix of scalars and charged scalars are calculated in the non-relativistic limit. The non- analytical parts of the scattering amplitudes yield the long range, low energy, leading quantum corrections. From the general relativity as an effective field theory the leading quantum corrections to the Newtonian gravity is constructed. General relativity combined with scalar QED yield the post- Newtonian and quantum corrections to the two-particle non-relativistic scattering matrix potential for charged scalar particles. The difference to other publications is finally discussed.