Abstract
We report on an ongoing study of photon amplitudes, graviton amplitudes and mixed photon-graviton amplitudes at tree-level using the worldline formalism. We explicitly recalculate the amplitude with one photon and one graviton coupled to a scalar propagator, relevant for graviton photoproduction. We comment on the factorization properties of this amplitude, and outline a generalization to similar processes involving more gravitons.
Highlights
We report on an ongoing study of photon amplitudes, graviton amplitudes and mixed photon-graviton amplitudes at tree-level using the worldline formalism
In the present manuscript we describe the first step, i.e. the worldline computation of the photon-graviton Compton scattering amplitude
Those extra terms are cancelled by the γ-pole diagram contributions. We hope that this observation eventually will lead to the establishment of some rules for finding the factorization properties of multi-graviton amplitudes without having to compute diagrams of the γ-pole type. In this contribution we presented our recent study of the Compton scattering amplitude for the process γ +s → g +s or its inverse
Summary
The worldline formalism is an approach to amplitude calculations in quantum field theory based on first quantization It has been introduced by Feynman[6] in 1950 for scalar and in 1951 for spinor quantum electrodynamics (QED) (for a review see Ref. 7). In the context of graviton scattering, the metric can be considered as the flat metric plus some fluctuation term which is a function of space-time, gμν (x(τ )) = ημν + κhμν(x(τ )). This world line action for curved space-time leads to considerable mathematical subtleties, as have been discussed extensively in Ref. 8. Let us mention that, at the one-loop level, there have already been several applications of this curved-space world line formalism, for example, the lowenergy limit of photon-graviton amplitudes,[10] gravitational corrections to the EulerHeisenberg Lagrangian,[11] and photon-graviton conversion in an electromagnetic field.[12]
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