Perturbation Calculation of Gravitational Potentials

概要

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The static gravitational potential for four-body system in the order of G^3 is calculated in the quantized theory. It is derived from the S-matrix elements for scattering of four spinless particles, among which gravitons are exchanged. Feynman's and de Donder's gauges are used for graviton propagator. The potential has contributions from the transverse-traceless part of the graviton field. The potential is different from that obtained in classical theory from the physically acceptable metric tensor derived in our previous paper under new coordinate conditions. Since all other known coordinate conditions such as de Donder's ones lead to divergent metric tensor at spatial infinity in the post-post-Newtonian approximation, it is not unreasonable that the two potentials become different first in this order of approximation.
理論物理学刊行会の論文
1973-12-25