Elementary Theory of Graviton Production Processes

• Published in: Annals of physics Vol. 238; no. 1; pp. 83 - 128
• Main Author: Gould, R.J.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.02.1995
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1006/aphy.1995.1016

A simplified formulation is outlined for the calculation of graviton processes by classical and quantum mechanical methods. The methods apply for processes involving radiation-field gravitons and for which the particles with finite mass are nonrelativistic. In the quantum mechanical formulation, perturbation diagrams are introduced-the nonrelativistic analog of Feynman diagrams in a covariant formulation; however, the exact meaning of the diagrams and vertices is different. For example, diagrams involving gravitons coupling to other interactions (vertices) are now important, in contrast to the usual cases in a covariant formulation. The methods are employed to calculate rates and cross sections for, in particular, the following processes: inner (graviton) bremsstrahlung, graviton production in scattering in a long-and short-range external potential, production in scattering of identical particles, and photograviton Compton scattering (γ + e → e + g). In the photograviton process, one diagram gives the main contribution; the diagram is associated with the graviton coupling to the vertex describing the photon interacting with the intrinsic magnetic moment of the electron. Graviton scattering is also considered. This is a higher-order process that requires an extension of the methods developed for its calculation. In the "Thomson limit" in which the graviton energy is small compared with the rest energy of the target particle, the main contribution to the cross section comes from a perturbation diagram associated with the exchange of a graviton between the target particle and the scattered graviton (a diagram with a three-graviton vertex). Photon scattering by an uncharged spinless particle is also considered, with the scattered photon exchanging a graviton with the target particle-the quantum mechanical version of light bending. For both of these processes, results are obtained that agree with previous calculations that started from a covariant formulation. A brief comparison is made with the classical calculation of the processes, and the validity domains of the classical and Born-approximation limits are discussed. The classical and Born formulas agree only in the limit of small scattering angles.