Abstract
A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field hμν(x) and position \( {x}_i^{\mu}\left({\tau}_i\right) \) of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection \( \Delta {p}_i^{\mu } \) from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.
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In memory of Sissi Plefka and Jürgen Steinhoff
ArXiv ePrint: 2010.02865
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Mogull, G., Plefka, J. & Steinhoff, J. Classical black hole scattering from a worldline quantum field theory. J. High Energ. Phys. 2021, 48 (2021). https://doi.org/10.1007/JHEP02(2021)048
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DOI: https://doi.org/10.1007/JHEP02(2021)048