Abstract
Using the implicit function theorem we demonstrate that solutions to the classical part of the relativistic Lippmann-Schwinger equation are in one-to-one correspondence with those of the energy equation of a relativistic two-body system. A corollary is that the scattering angle can be computed from the amplitude itself, without having to introduce a potential. All results are universal and provide for the case of general relativity a very simple formula for the scattering angle in terms of the classical part of the amplitude, to any order in the post-Minkowskian expansion.
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Bjerrum-Bohr, N., Cristofoli, A. & Damgaard, P.H. Post-Minkowskian scattering angle in Einstein gravity. J. High Energ. Phys. 2020, 38 (2020). https://doi.org/10.1007/JHEP08(2020)038
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DOI: https://doi.org/10.1007/JHEP08(2020)038