On the role of gravitational fields in some elementary particle processes

Abstract

With the aid of a suitable perturbation formalism, the effect of an external gravitational field on elementary particle processes is investigated. Electromagnetic bremsstrahlung by charged scalar particle waves is treated and the dependence of the result on the inserted data and their empirical limits is analised. Application of the results to gravitational bremsstrahlung by particles of vanishing rest-mass is made. On the basis of these results, gravitational radiation from elementary particle processes is shown to be negligible. Some quantum electrodynamic processes of higher order, with closed loop diagrams are treated in curved space and the removal of their infinities by renormalization is discussed. Part of the matrix element for the process of photon trisection into three photons, has been evaluated and an upper limit for the cross-section of this process has been obtained in first order approximation in the external gravitational field. The magnitude of certain contributions from higher order terms has been estimated, but complete conclusions have not yet been obtained. A number of other processes, involving particles with spin and their radiative corrections are treated or discussed. Among the cross-sections of these processes, in first order perturbation only that for the trisection of photons becomes significant at the empirical energy limit: these theoretical results at present deny experimental possibilities. The role of terms of higher order is not yet known. Experimental possibilities for obtaining improved knowledge of the empirical upper limit of the energy losses produced on photons are suggested. General empirical aspects of the theoretical results are discussed. The Appendix contains an auxiliary theorem on a relation between the second derivatives of the metric tensor and the Riemann-Christoffel tensor at points, where geodesic co-ordinates are introduced.