Abstract
We demonstrate the equivalence between observables in the KMOC and worldline formalisms for classical general relativity, highlighting the relation between the initial conditions in the two frameworks and how the Keldysh-Schwinger in-in formalism is contained in both of them even though the KMOC representation conventionally leads to the evaluation of scattering amplitudes with Feynman propagators. The relationship between the two approaches is illustrated in detail for the momentum kick at second Post-Minkowskian order.
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Acknowledgments
We thank Jan Plefka for discussions. P.H.D. and P.V. would like to thank CERN Theory Department and LAPTh, respectively, for the hospitality during the completion of this work. P.V. is grateful to the Mainz Institute for Theoretical Physics (MITP) of the Cluster of Excellence PRIMA+ (Project ID 39083149), for its hospitality and its partial support 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. The relation between KMOC and worldline formalisms for classical gravity. J. High Energ. Phys. 2023, 59 (2023). https://doi.org/10.1007/JHEP09(2023)059
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DOI: https://doi.org/10.1007/JHEP09(2023)059