Abstract
An exponential representation of the S-matrix provides a natural framework for understanding the semi-classical limit of scattering amplitudes. While sharing some similarities with the eikonal formalism it differs from it in details. Computationally, rules are simple because pieces that must be subtracted are given by combinations of unitarity cuts. Analyzing classical gravitational scattering to third Post-Minkowskian order in both maximal supergravity and Einstein gravity we find agreement with other approaches, including the contributions from radiation reaction terms. The kinematical relation for the two-body problem in isotropic coordinates follows immediately from this procedure, again with the inclusion of radiation reaction pieces up to third Post-Minkowskian order.
Highlights
Et al [17] we here wish to explore the possibility of using the WKB limit of relativistic quantum field theories to derive in an alternative manner the classical scattering of two massive objects in general relativity from scattering amplitudes
Analyzing classical gravitational scattering to third Post-Minkowskian order in both maximal supergravity and Einstein gravity we find agreement with other approaches, including the contributions from radiation reaction terms
We shall check our proposal to third Post-Minkowskian order for both maximal supergravity and Einstein gravity, and we shall point out a simple link to the potential from the Hamiltonian formalism
Summary
States are saturated by two scalars and one graviton for the term involving T0rad and just two scalars in the remaining terms At higher orders these relations get increasingly complicated the two body matrix elements of Nare always real. reality of the matrix elements For each Ni the subtractions of eq (2.7) remove precisely all imaginary parts from the matrix element of Ti. The expansions (2.10) have nice diagrammatic interpretations in terms of unitarity cuts. It is interesting to compare with the manner in which terms exponentiate in the eikonal approach where the additional subtractions of imaginary parts of eq (2.15) occur as part of the lower-point iterations, instead, as here, in one go because of unitarity To summarize this part, the matrix element of any Ni is manifestly real. We will check the results up to third Post-Minkowskian order and will simultaneously show that this method is not limited to the potential region
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