Abstract
By combining the KMOC-formalism with the exponential representation of the scattering matrix we show that the two-body scattering angle is given by the corresponding matrix element of the exponential representation. This holds to all orders in the Post-Minkowskian expansion of gravity when restricted to the conservative sector. Once gravitational radiation is taken into account new terms correcting this relationship appear starting at fourth Post-Minkowskian order. A systematic expansion of the momentum kick is provided to any order, thus illustrating the iterative structure that partly recycles terms from lower orders in the Post-Minkowskian expansion. We provide explicit results for this computation to fourth Post-Minkowskian order, the first complete calculation at this order based on scattering amplitudes.
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Acknowledgments
We thank Thibault Damour for comments. P.V. would like to thank the LAPTh for the hospitality during the completion of this work. The work of P.H.D. was supported in part by DFF grant 0135-00089A, the work of E.R.H. was supported by the Rozenthal Foundation and ERC Starting Grant No. 757978 from the European Research Council, and the research of P.V. has received funding from the ANR grant “SMAGP” ANR-20-CE40-0026-01.
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Damgaard, P.H., Hansen, E.R., Planté, L. et al. Classical observables from the exponential representation of the gravitational S-matrix. J. High Energ. Phys. 2023, 183 (2023). https://doi.org/10.1007/JHEP09(2023)183
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DOI: https://doi.org/10.1007/JHEP09(2023)183