Calculational aspects of quantum gravity

Weak field gravitational effects in the context of Schwinger's Source Theory are investigated. The first type of calculation considered is particle scattering from a weak, immobile gravitational scattering center with T/sup oo/(x) - m delta(x), T/sup oi/(x) = T/sup ij/(x) = 0. Physical cross sections for scalar, vector (including photon) and graviton scattering from the weak source are developed. Next, gravitational scattering events between identical and non-identical scalar particles are considered. The last cross section derived is for scalar-graviton scattering. These gravitational scattering calculations are shown to be consistent with the earlier fixed-source interactions. The subject of quantum gravitational corrections to physical processes is begun by calculating the first order correction to the photon propagation function. This yields a tensor quantity used extensively in later calculations and gives a modification to the usual electromagnetic interaction between static charges at high energies. A series of causal calculations, aimed at isolating the gravitational contribution to the electron (or muon or tau) magnetic moment is then discribed. Two of the methods involve a quantized electromagnetic field; these causal calculations fail to produce a finite answer because gravitational gauge invariance does not connect the various diagrams into a unified amplitude. The third causal calculation, which uses a classical external electromagnetic field, cures this problem and produces a finite answer which, however, is not guaranteed to be unique. The final noncausal calculation again demonstrates the finiteness of the gravitatonal magnetic moment, but argues that this quantity is not uniquely determined by physical requirements