{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T07:37:34Z","timestamp":1777361854792,"version":"3.51.4"},"reference-count":144,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T00:00:00Z","timestamp":1612483200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T00:00:00Z","timestamp":1612483200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. High Energ. Phys."],"abstract":"<jats:title>A<jats:sc>bstract<\/jats:sc>\n                     <\/jats:title><jats:p>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 <jats:italic>h<\/jats:italic><jats:sub><jats:italic>\u03bc\u03bd<\/jats:italic><\/jats:sub>(<jats:italic>x<\/jats:italic>) and position <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {x}_i^{\\mu}\\left({\\tau}_i\\right) $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msubsup>\n                    <mml:mi>x<\/mml:mi>\n                    <mml:mi>i<\/mml:mi>\n                    <mml:mi>\u03bc<\/mml:mi>\n                  <\/mml:msubsup>\n                  <mml:mfenced>\n                    <mml:msub>\n                      <mml:mi>\u03c4<\/mml:mi>\n                      <mml:mi>i<\/mml:mi>\n                    <\/mml:msub>\n                  <\/mml:mfenced>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation \u2329<jats:italic>h<\/jats:italic><jats:sup><jats:italic>\u03bcv<\/jats:italic><\/jats:sup>(<jats:italic>k<\/jats:italic>)\u232a and 2PM two-body deflection <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \\Delta {p}_i^{\\mu } $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u0394<\/mml:mi>\n                  <mml:msubsup>\n                    <mml:mi>p<\/mml:mi>\n                    <mml:mi>i<\/mml:mi>\n                    <mml:mi>\u03bc<\/mml:mi>\n                  <\/mml:msubsup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 <jats:italic>\u2192<\/jats:italic> 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.<\/jats:p>","DOI":"10.1007\/jhep02(2021)048","type":"journal-article","created":{"date-parts":[[2021,2,6]],"date-time":"2021-02-06T14:22:40Z","timestamp":1612621360000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":232,"title":["Classical black hole scattering from a worldline quantum field theory"],"prefix":"10.1007","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3070-5717","authenticated-orcid":false,"given":"Gustav","family":"Mogull","sequence":"first","affiliation":[]},{"given":"Jan","family":"Plefka","sequence":"additional","affiliation":[]},{"given":"Jan","family":"Steinhoff","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,2,5]]},"reference":[{"key":"14774_CR1","unstructured":"S. Chandrasekhar, Beauty and the quest for beauty in science, talk given at the International Symposium in Honor of Robert R. Wilson, April 27, Boston, U.S.A. (1979)."},{"key":"14774_CR2","doi-asserted-by":"publisher","first-page":"454001","DOI":"10.1088\/1751-8113\/44\/45\/454001","volume":"44","author":"LJ Dixon","year":"2011","unstructured":"L.J. Dixon, Scattering amplitudes: the most perfect microscopic structures in the universe, J. Phys. A 44 (2011) 454001 [arXiv:1105.0771] [INSPIRE].","journal-title":"J. Phys. A"},{"key":"14774_CR3","unstructured":"LIGO Scientific, Virgo collaboration, Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116 (2016) 061102 [arXiv:1602.03837] [INSPIRE]."},{"key":"14774_CR4","unstructured":"LIGO Scientific, Virgo collaboration, GW170817: observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119 (2017) 161101 [arXiv:1710.05832] [INSPIRE]."},{"key":"14774_CR5","unstructured":"LIGO Scientific, Virgo collaboration, GWTC-1: a gravitational-wave transient catalog of compact binary mergers observed by LIGO and Virgo during the first and second observing runs, Phys. Rev. X 9 (2019) 031040 [arXiv:1811.12907] [INSPIRE]."},{"key":"14774_CR6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.023151","volume":"2","author":"M P\u00fcrrer","year":"2020","unstructured":"M. P\u00fcrrer and C.-J. Haster, Gravitational waveform accuracy requirements for future ground-based detectors, Phys. Rev. Res. 2 (2020) 023151 [arXiv:1912.10055] [INSPIRE].","journal-title":"Phys. Rev. Res."},{"key":"14774_CR7","doi-asserted-by":"publisher","first-page":"2","DOI":"10.12942\/lrr-2014-2","volume":"17","author":"L Blanchet","year":"2014","unstructured":"L. Blanchet, Gravitational radiation from post-Newtonian sources and inspiralling compact binaries, Living Rev. Rel. 17 (2014) 2 [arXiv:1310.1528] [INSPIRE].","journal-title":"Living Rev. Rel."},{"key":"14774_CR8","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1007\/s41114-018-0016-5","volume":"21","author":"G Sch\u00e4fer","year":"2018","unstructured":"G. Sch\u00e4fer and P. Jaranowski, Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries, Living Rev. Rel. 21 (2018) 7 [arXiv:1805.07240] [INSPIRE].","journal-title":"Living Rev. Rel."},{"key":"14774_CR9","doi-asserted-by":"publisher","first-page":"2","DOI":"10.12942\/lrr-2007-2","volume":"10","author":"T Futamase","year":"2007","unstructured":"T. Futamase and Y. Itoh, The post-Newtonian approximation for relativistic compact binaries, Living Rev. Rel. 10 (2007) 2 [INSPIRE].","journal-title":"Living Rev. Rel."},{"key":"14774_CR10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.62.124015","volume":"62","author":"ME Pati","year":"2000","unstructured":"M.E. Pati and C.M. Will, Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. 1. Foundations, Phys. Rev. D 62 (2000) 124015 [gr-qc\/0007087] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR11","doi-asserted-by":"publisher","first-page":"963","DOI":"10.1007\/BF00756073","volume":"13","author":"L Bel","year":"1981","unstructured":"L. Bel, T. Damour, N. Deruelle, J. Ib\u00e1\u00f1ez and J. Martin, Poincar\u00e9-invariant gravitational field and equations of motion of two pointlike objects: the postlinear approximation of general relativity, Gen. Rel. Grav. 13 (1981) 963 [INSPIRE].","journal-title":"Gen. Rel. Grav."},{"key":"14774_CR12","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1002\/prop.2190330802","volume":"33","author":"K Westpfahl","year":"1985","unstructured":"K. Westpfahl, High-speed scattering of charged and uncharged particles in general relativity, Fortsch. Phys. 33 (1985) 417 [INSPIRE].","journal-title":"Fortsch. Phys."},{"key":"14774_CR13","doi-asserted-by":"publisher","first-page":"104029","DOI":"10.1103\/PhysRevD.73.104029","volume":"73","author":"WD Goldberger","year":"2006","unstructured":"W.D. Goldberger and I.Z. Rothstein, An effective field theory of gravity for extended objects, Phys. Rev. D 73 (2006) 104029 [hep-th\/0409156] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR14","doi-asserted-by":"crossref","unstructured":"W.D. Goldberger and I.Z. Rothstein, Towers of gravitational theories, Gen. Rel. Grav. 38 (2006) 1537 [Int. J. Mod. Phys. D 15 (2006) 2293] [hep-th\/0605238] [INSPIRE].","DOI":"10.1007\/s10714-006-0345-7"},{"key":"14774_CR15","doi-asserted-by":"publisher","first-page":"124015","DOI":"10.1103\/PhysRevD.81.124015","volume":"81","author":"WD Goldberger","year":"2010","unstructured":"W.D. Goldberger and A. Ross, Gravitational radiative corrections from effective field theory, Phys. Rev. D 81 (2010) 124015 [arXiv:0912.4254] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR16","doi-asserted-by":"publisher","first-page":"145011","DOI":"10.1088\/0264-9381\/25\/14\/145011","volume":"25","author":"B Kol","year":"2008","unstructured":"B. Kol and M. Smolkin, Non-relativistic gravitation: from Newton to Einstein and back, Class. Quant. Grav. 25 (2008) 145011 [arXiv:0712.4116] [INSPIRE].","journal-title":"Class. Quant. Grav."},{"key":"14774_CR17","doi-asserted-by":"crossref","unstructured":"W.D. Goldberger, Les Houches lectures on effective field theories and gravitational radiation, in the proceedings of Les Houches Summer School \u2014 Session 86: Particle Physics and Cosmology: The Fabric of Spacetime, July 31\u2013August 25, Les Houches, France (2007), hep-ph\/0701129 [INSPIRE].","DOI":"10.1016\/S0924-8099(07)80033-3"},{"key":"14774_CR18","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/31\/4\/043001","volume":"31","author":"S Foffa","year":"2014","unstructured":"S. Foffa and R. Sturani, Effective field theory methods to model compact binaries, Class. Quant. Grav. 31 (2014) 043001 [arXiv:1309.3474] [INSPIRE].","journal-title":"Class. Quant. Grav."},{"key":"14774_CR19","doi-asserted-by":"publisher","first-page":"1726","DOI":"10.1007\/s10714-014-1726-y","volume":"46","author":"IZ Rothstein","year":"2014","unstructured":"I.Z. Rothstein, Progress in effective field theory approach to the binary inspiral problem, Gen. Rel. Grav. 46 (2014) 1726 [INSPIRE].","journal-title":"Gen. Rel. Grav."},{"key":"14774_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2016.04.003","volume":"633","author":"RA Porto","year":"2016","unstructured":"R.A. Porto, The effective field theorist\u2019s approach to gravitational dynamics, Phys. Rept. 633 (2016) 1 [arXiv:1601.04914] [INSPIRE].","journal-title":"Phys. Rept."},{"key":"14774_CR21","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6633\/ab12bc","volume":"83","author":"M Levi","year":"2020","unstructured":"M. Levi, Effective field theories of post-Newtonian gravity: a comprehensive review, Rept. Prog. Phys. 83 (2020) 075901 [arXiv:1807.01699] [INSPIRE].","journal-title":"Rept. Prog. Phys."},{"key":"14774_CR22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.89.064058","volume":"89","author":"T Damour","year":"2014","unstructured":"T. Damour, P. Jaranowski and G. Sch\u00e4fer, Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems, Phys. Rev. D 89 (2014) 064058 [arXiv:1401.4548] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.93.084014","volume":"93","author":"T Damour","year":"2016","unstructured":"T. Damour, P. Jaranowski and G. Sch\u00e4fer, Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity, Phys. Rev. D 93 (2016) 084014 [arXiv:1601.01283] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.95.044026","volume":"95","author":"L Bernard","year":"2017","unstructured":"L. Bernard, L. Blanchet, A. Boh\u00e9, G. Faye and S. Marsat, Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order, Phys. Rev. D 95 (2017) 044026 [arXiv:1610.07934] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR25","doi-asserted-by":"publisher","first-page":"104009","DOI":"10.1103\/PhysRevD.95.104009","volume":"95","author":"S Foffa","year":"2017","unstructured":"S. Foffa, P. Mastrolia, R. Sturani and C. Sturm, Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant, Phys. Rev. D 95 (2017) 104009 [arXiv:1612.00482] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.95.084005","volume":"95","author":"T Damour","year":"2017","unstructured":"T. Damour and P. Jaranowski, Four-loop static contribution to the gravitational interaction potential of two point masses, Phys. Rev. D 95 (2017) 084005 [arXiv:1701.02645] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.100.024047","volume":"100","author":"S Foffa","year":"2019","unstructured":"S. Foffa and R. Sturani, Conservative dynamics of binary systems to fourth post-Newtonian order in the EFT approach I: regularized Lagrangian, Phys. Rev. D 100 (2019) 024047 [arXiv:1903.05113] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.100.024048","volume":"100","author":"S Foffa","year":"2019","unstructured":"S. Foffa, R.A. Porto, I. Rothstein and R. Sturani, Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: renormalized Lagrangian, Phys. Rev. D 100 (2019) 024048 [arXiv:1903.05118] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR29","doi-asserted-by":"publisher","first-page":"115041","DOI":"10.1016\/j.nuclphysb.2020.115041","volume":"955","author":"J Bl\u00fcmlein","year":"2020","unstructured":"J. Bl\u00fcmlein, A. Maier, P. Marquard and G. Sch\u00e4fer, Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach, Nucl. Phys. B 955 (2020) 115041 [arXiv:2003.01692] [INSPIRE].","journal-title":"Nucl. Phys. B"},{"key":"14774_CR30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.96.024062","volume":"96","author":"RA Porto","year":"2017","unstructured":"R.A. Porto and I.Z. Rothstein, Apparent ambiguities in the post-Newtonian expansion for binary systems, Phys. Rev. D 96 (2017) 024062 [arXiv:1703.06433] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.97.044023","volume":"97","author":"T Marchand","year":"2018","unstructured":"T. Marchand, L. Bernard, L. Blanchet and G. Faye, Ambiguity-free completion of the equations of motion of compact binary systems at the fourth post-Newtonian order, Phys. Rev. D 97 (2018) 044023 [arXiv:1707.09289] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR32","doi-asserted-by":"publisher","first-page":"124010","DOI":"10.1103\/PhysRevD.93.124010","volume":"93","author":"CR Galley","year":"2016","unstructured":"C.R. Galley, A.K. Leibovich, R.A. Porto and A. Ross, Tail effect in gravitational radiation reaction: time nonlocality and renormalization group evolution, Phys. Rev. D 93 (2016) 124010 [arXiv:1511.07379] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR33","doi-asserted-by":"publisher","first-page":"241605","DOI":"10.1103\/PhysRevLett.122.241605","volume":"122","author":"S Foffa","year":"2019","unstructured":"S. Foffa, P. Mastrolia, R. Sturani, C. Sturm and W.J. Torres Bobadilla, Static two-body potential at fifth post-Newtonian order, Phys. Rev. Lett. 122 (2019) 241605 [arXiv:1902.10571] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"14774_CR34","doi-asserted-by":"publisher","first-page":"135100","DOI":"10.1016\/j.physletb.2019.135100","volume":"800","author":"J Bl\u00fcmlein","year":"2020","unstructured":"J. Bl\u00fcmlein, A. Maier and P. Marquard, Five-loop static contribution to the gravitational interaction potential of two point masses, Phys. Lett. B 800 (2020) 135100 [arXiv:1902.11180] [INSPIRE].","journal-title":"Phys. Lett. B"},{"key":"14774_CR35","doi-asserted-by":"publisher","first-page":"231104","DOI":"10.1103\/PhysRevLett.123.231104","volume":"123","author":"D Bini","year":"2019","unstructured":"D. Bini, T. Damour and A. Geralico, Novel approach to binary dynamics: application to the fifth post-Newtonian level, Phys. Rev. Lett. 123 (2019) 231104 [arXiv:1909.02375] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"14774_CR36","unstructured":"J. Bl\u00fcmlein, A. Maier, P. Marquard and G. Sch\u00e4fer, The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions, arXiv:2010.13672"},{"key":"14774_CR37","doi-asserted-by":"publisher","first-page":"135496","DOI":"10.1016\/j.physletb.2020.135496","volume":"807","author":"J Bl\u00fcmlein","year":"2020","unstructured":"J. Bl\u00fcmlein, A. Maier, P. Marquard and G. Sch\u00e4fer, Testing binary dynamics in gravity at the sixth post-Newtonian level, Phys. Lett. B 807 (2020) 135496 [arXiv:2003.07145] [INSPIRE].","journal-title":"Phys. Lett. B"},{"key":"14774_CR38","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1007\/JHEP06(2020)144","volume":"06","author":"C Cheung","year":"2020","unstructured":"C. Cheung and M.P. Solon, Classical gravitational scattering at $$ \\mathcal{O}\\left({G}^3\\right) $$ from Feynman diagrams, JHEP 06 (2020) 144 [arXiv:2003.08351] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR39","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.102.024061","volume":"102","author":"D Bini","year":"2020","unstructured":"D. Bini, T. Damour and A. Geralico, Sixth post-Newtonian local-in-time dynamics of binary systems, Phys. Rev. D 102 (2020) 024061 [arXiv:2004.05407] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.102.024062","volume":"102","author":"D Bini","year":"2020","unstructured":"D. Bini, T. Damour and A. Geralico, Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders, Phys. Rev. D 102 (2020) 024062 [arXiv:2003.11891] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR41","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.102.084047","volume":"102","author":"D Bini","year":"2020","unstructured":"D. Bini, T. Damour and A. Geralico, Sixth post-Newtonian nonlocal-in-time dynamics of binary systems, Phys. Rev. D 102 (2020) 084047 [arXiv:2007.11239] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR42","unstructured":"D. Bini, T. Damour, A. Geralico, S. Laporta and P. Mastrolia, Gravitational dynamics at O(G6): perturbative gravitational scattering meets experimental mathematics, arXiv:2008.09389 [INSPIRE]."},{"key":"14774_CR43","doi-asserted-by":"crossref","unstructured":"L. Blanchet, B.R. Iyer and B. Joguet, Gravitational waves from inspiralling compact binaries: energy flux to third postNewtonian order, Phys. Rev. D 65 (2002) 064005 [Erratum ibid. 71 (2005) 129903] [gr-qc\/0105098] [INSPIRE].","DOI":"10.1103\/PhysRevD.65.064005"},{"key":"14774_CR44","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.93.091101","volume":"93","author":"L Blanchet","year":"2004","unstructured":"L. Blanchet, T. Damour, G. Esposito-Farese and B.R. Iyer, Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order, Phys. Rev. Lett. 93 (2004) 091101 [gr-qc\/0406012] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"14774_CR45","doi-asserted-by":"crossref","unstructured":"L. Blanchet, G. Faye, B.R. Iyer and S. Sinha, The third post-Newtonian gravitational wave polarisations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits, Class. Quant. Grav. 25 (2008) 165003 [Erratum ibid. 29 (2012) 239501] [arXiv:0802.1249] [INSPIRE].","DOI":"10.1088\/0264-9381\/25\/16\/165003"},{"key":"14774_CR46","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.101.084058","volume":"101","author":"AK Leibovich","year":"2020","unstructured":"A.K. Leibovich, N.T. Maia, I.Z. Rothstein and Z. Yang, Second post-Newtonian order radiative dynamics of inspiralling compact binaries in the Effective Field Theory approach, Phys. Rev. D 101 (2020) 084058 [arXiv:1912.12546] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR47","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.73.104031","volume":"73","author":"RA Porto","year":"2006","unstructured":"R.A. Porto, Post-Newtonian corrections to the motion of spinning bodies in NRGR, Phys. Rev. D 73 (2006) 104031 [gr-qc\/0511061] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR48","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/JHEP09(2015)219","volume":"09","author":"M Levi","year":"2015","unstructured":"M. Levi and J. Steinhoff, Spinning gravitating objects in the effective field theory in the post-Newtonian scheme, JHEP 09 (2015) 219 [arXiv:1501.04956] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR49","unstructured":"M. Levi, A.J. Mcleod and M. Von Hippel, N3 LO gravitational spin-orbit coupling at order G4, arXiv:2003.02827 [INSPIRE]."},{"key":"14774_CR50","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.125.011103","volume":"125","author":"A Antonelli","year":"2020","unstructured":"A. Antonelli, C. Kavanagh, M. Khalil, J. Steinhoff and J. Vines, Gravitational spin-orbit coupling through third-subleading post-Newtonian order: from first-order self-force to arbitrary mass ratios, Phys. Rev. Lett. 125 (2020) 011103 [arXiv:2003.11391] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"14774_CR51","unstructured":"M. Levi and J. Steinhoff, Complete conservative dynamics for inspiralling compact binaries with spins at fourth post-Newtonian order, arXiv:1607.04252 [INSPIRE]."},{"key":"14774_CR52","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.97.021101","volume":"97","author":"RA Porto","year":"2006","unstructured":"R.A. Porto and I.Z. Rothstein, The hyperfine Einstein-Infeld-Hoffmann potential, Phys. Rev. Lett. 97 (2006) 021101 [gr-qc\/0604099] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"14774_CR53","doi-asserted-by":"crossref","unstructured":"R.A. Porto and I.Z. Rothstein, Spin(1)Spin(2) effects in the motion of inspiralling compact binaries at third order in the post-Newtonian expansion, Phys. Rev. D 78 (2008) 044012 [Erratum ibid. 81 (2010) 029904] [arXiv:0802.0720] [INSPIRE].","DOI":"10.1103\/PhysRevD.78.044012"},{"key":"14774_CR54","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.82.064029","volume":"82","author":"M Levi","year":"2010","unstructured":"M. Levi, Next to leading order gravitational Spin(1)-Spin(2) coupling with Kaluza-Klein reduction, Phys. Rev. D 82 (2010) 064029 [arXiv:0802.1508] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR55","doi-asserted-by":"crossref","unstructured":"R.A. Porto and I.Z. Rothstein, Next to leading order Spin(1)-Spin(1) effects in the motion of inspiralling compact binaries, Phys. Rev. D 78 (2008) 044013 [Erratum ibid. 81 (2010) 029905] [arXiv:0804.0260] [INSPIRE].","DOI":"10.1103\/PhysRevD.78.044013"},{"key":"14774_CR56","doi-asserted-by":"publisher","first-page":"205001","DOI":"10.1088\/0264-9381\/27\/20\/205001","volume":"27","author":"RA Porto","year":"2010","unstructured":"R.A. Porto, Next to leading order spin-orbit effects in the motion of inspiralling compact binaries, Class. Quant. Grav. 27 (2010) 205001 [arXiv:1005.5730] [INSPIRE].","journal-title":"Class. Quant. Grav."},{"key":"14774_CR57","unstructured":"D.L. Perrodin, Subleading spin-orbit correction to the Newtonian potential in effective field theory formalism, in the proceedings of the 12th Marcel Grossmann Meeting on General Relativity, July 20\u201326, Rio de Janeiro, Brasil (2010) [arXiv:1005.0634] [INSPIRE]."},{"key":"14774_CR58","doi-asserted-by":"publisher","first-page":"104004","DOI":"10.1103\/PhysRevD.82.104004","volume":"82","author":"M Levi","year":"2010","unstructured":"M. Levi, Next to leading order gravitational spin-orbit coupling in an effective field theory approach, Phys. Rev. D 82 (2010) 104004 [arXiv:1006.4139] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR59","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.93.084054","volume":"93","author":"CK Mishra","year":"2016","unstructured":"C.K. Mishra, A. Kela, K.G. Arun and G. Faye, Ready-to-use post-Newtonian gravitational waveforms for binary black holes with nonprecessing spins: An update, Phys. Rev. D 93 (2016) 084054 [arXiv:1601.05588] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR60","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.87.044009","volume":"87","author":"A Buonanno","year":"2013","unstructured":"A. Buonanno, G. Faye and T. Hinderer, Spin effects on gravitational waves from inspiraling compact binaries at second post-Newtonian order, Phys. Rev. D 87 (2013) 044009 [arXiv:1209.6349] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR61","doi-asserted-by":"publisher","first-page":"009","DOI":"10.1088\/1475-7516\/2011\/03\/009","volume":"03","author":"RA Porto","year":"2011","unstructured":"R.A. Porto, A. Ross and I.Z. Rothstein, Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order, JCAP 03 (2011) 009 [arXiv:1007.1312] [INSPIRE].","journal-title":"JCAP"},{"key":"14774_CR62","doi-asserted-by":"publisher","first-page":"028","DOI":"10.1088\/1475-7516\/2012\/09\/028","volume":"09","author":"RA Porto","year":"2012","unstructured":"R.A. Porto, A. Ross and I.Z. Rothstein, Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 post-Newtonian order, JCAP 09 (2012) 028 [arXiv:1203.2962] [INSPIRE].","journal-title":"JCAP"},{"key":"14774_CR63","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.96.084064","volume":"96","author":"NT Maia","year":"2017","unstructured":"N.T. Maia, C.R. Galley, A.K. Leibovich and R.A. Porto, Radiation reaction for spinning bodies in effective field theory I: spin-orbit effects, Phys. Rev. D 96 (2017) 084064 [arXiv:1705.07934] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR64","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.96.084065","volume":"96","author":"NT Maia","year":"2017","unstructured":"N.T. Maia, C.R. Galley, A.K. Leibovich and R.A. Porto, Radiation reaction for spinning bodies in effective field theory II: spin-spin effects, Phys. Rev. D 96 (2017) 084065 [arXiv:1705.07938] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR65","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1007\/JHEP11(2020)106","volume":"11","author":"G K\u00e4lin","year":"2020","unstructured":"G. K\u00e4lin and R.A. Porto, Post-Minkowskian effective field theory for conservative binary dynamics, JHEP 11 (2020) 106 [arXiv:2006.01184] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR66","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.101.044039","volume":"101","author":"D Bini","year":"2020","unstructured":"D. Bini, T. Damour and A. Geralico, Scattering of tidally interacting bodies in post-Minkowskian gravity, Phys. Rev. D 101 (2020) 044039 [arXiv:2001.00352] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR67","doi-asserted-by":"publisher","first-page":"191601","DOI":"10.1103\/PhysRevLett.125.191601","volume":"125","author":"C Cheung","year":"2020","unstructured":"C. Cheung and M.P. Solon, Tidal effects in the post-Minkowskian expansion, Phys. Rev. Lett. 125 (2020) 191601 [arXiv:2006.06665] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"14774_CR68","doi-asserted-by":"publisher","first-page":"124025","DOI":"10.1103\/PhysRevD.102.124025","volume":"102","author":"G K\u00e4lin","year":"2020","unstructured":"G. K\u00e4lin, Z. Liu and R.A. Porto, Conservative tidal effects in compact binary systems to next-to-leading post-Minkowskian order, Phys. Rev. D 102 (2020) 124025 [arXiv:2008.06047] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR69","doi-asserted-by":"publisher","first-page":"024","DOI":"10.1007\/JHEP12(2020)024","volume":"12","author":"K Haddad","year":"2020","unstructured":"K. Haddad and A. Helset, Tidal effects in quantum field theory, JHEP 12 (2020) 024 [arXiv:2008.04920] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR70","doi-asserted-by":"publisher","first-page":"261103","DOI":"10.1103\/PhysRevLett.125.261103","volume":"125","author":"G K\u00e4lin","year":"2020","unstructured":"G. K\u00e4lin, Z. Liu and R.A. Porto, Conservative dynamics of binary systems to third post-Minkowskian order from the effective field theory approach, Phys. Rev. Lett. 125 (2020) 261103 [arXiv:2007.04977] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"14774_CR71","doi-asserted-by":"publisher","first-page":"251101","DOI":"10.1103\/PhysRevLett.100.251101","volume":"100","author":"T Ledvinka","year":"2008","unstructured":"T. Ledvinka, G. Schaefer and J. Bicak, Relativistic closed-form Hamiltonian for many-body gravitating systems in the post-Minkowskian approximation, Phys. Rev. Lett. 100 (2008) 251101 [arXiv:0807.0214] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"14774_CR72","doi-asserted-by":"publisher","first-page":"104015","DOI":"10.1103\/PhysRevD.94.104015","volume":"94","author":"T Damour","year":"2016","unstructured":"T. Damour, Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory, Phys. Rev. D 94 (2016) 104015 [arXiv:1609.00354] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR73","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.98.084005","volume":"98","author":"L Blanchet","year":"2018","unstructured":"L. Blanchet and A.S. Fokas, Equations of motion of self-gravitating N -body systems in the first post-Minkowskian approximation, Phys. Rev. D 98 (2018) 084005 [arXiv:1806.08347] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR74","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1086\/155576","volume":"217","author":"SJ Kovacs","year":"1977","unstructured":"S.J. Kovacs and K.S. Thorne, The generation of gravitational waves. III. Derivation of bremsstrahlung formulae, Astrophys. J. 217 (1977) 252.","journal-title":"Astrophys. J."},{"key":"14774_CR75","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1086\/156350","volume":"224","author":"SJ Kovacs","year":"1978","unstructured":"S.J. Kovacs and K.S. Thorne, The generation of gravitational waves. IV. Bremsstrahlung, Astrophys. J. 224 (1978) 62.","journal-title":"Astrophys. J."},{"key":"14774_CR76","doi-asserted-by":"publisher","first-page":"104038","DOI":"10.1103\/PhysRevD.96.104038","volume":"96","author":"D Bini","year":"2017","unstructured":"D. Bini and T. Damour, Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation and effective one-body theory, Phys. Rev. D 96 (2017) 104038 [arXiv:1709.00590] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR77","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6382\/aaa3a8","volume":"35","author":"J Vines","year":"2018","unstructured":"J. Vines, Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings, Class. Quant. Grav. 35 (2018) 084002 [arXiv:1709.06016] [INSPIRE].","journal-title":"Class. Quant. Grav."},{"key":"14774_CR78","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.98.044036","volume":"98","author":"D Bini","year":"2018","unstructured":"D. Bini and T. Damour, Gravitational spin-orbit coupling in binary systems at the second post-Minkowskian approximation, Phys. Rev. D 98 (2018) 044036 [arXiv:1805.10809] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR79","doi-asserted-by":"publisher","first-page":"1587","DOI":"10.1143\/PTP.46.1587","volume":"46","author":"Y Iwasaki","year":"1971","unstructured":"Y. Iwasaki, Quantum theory of gravitation vs. classical theory \u2014 Fourth-order potential, Prog. Theor. Phys. 46 (1971) 1587 [INSPIRE].","journal-title":"Prog. Theor. Phys."},{"key":"14774_CR80","doi-asserted-by":"publisher","first-page":"2317","DOI":"10.1103\/PhysRevD.7.2317","volume":"7","author":"MJ Duff","year":"1973","unstructured":"M.J. Duff, Quantum tree graphs and the Schwarzschild solution, Phys. Rev. D 7 (1973) 2317 [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR81","doi-asserted-by":"publisher","first-page":"201602","DOI":"10.1103\/PhysRevLett.93.201602","volume":"93","author":"BR Holstein","year":"2004","unstructured":"B.R. Holstein and J.F. Donoghue, Classical physics and quantum loops, Phys. Rev. Lett. 93 (2004) 201602 [hep-th\/0405239] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"14774_CR82","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.nuclphysb.2013.09.007","volume":"877","author":"D Neill","year":"2013","unstructured":"D. Neill and I.Z. Rothstein, Classical space-times from the S-matrix, Nucl. Phys. B 877 (2013) 177 [arXiv:1304.7263] [INSPIRE].","journal-title":"Nucl. Phys. B"},{"key":"14774_CR83","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/JHEP02(2014)111","volume":"02","author":"NEJ Bjerrum-Bohr","year":"2014","unstructured":"N.E.J. Bjerrum-Bohr, J.F. Donoghue and P. Vanhove, On-shell techniques and universal results in quantum gravity, JHEP 02 (2014) 111 [arXiv:1309.0804] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR84","doi-asserted-by":"publisher","first-page":"044","DOI":"10.1007\/JHEP03(2018)044","volume":"03","author":"A Luna","year":"2018","unstructured":"A. Luna, I. Nicholson, D. O\u2019Connell and C.D. White, Inelastic black hole scattering from charged scalar amplitudes, JHEP 03 (2018) 044 [arXiv:1711.03901] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR85","doi-asserted-by":"publisher","first-page":"171601","DOI":"10.1103\/PhysRevLett.121.171601","volume":"121","author":"NEJ Bjerrum-Bohr","year":"2018","unstructured":"N.E.J. Bjerrum-Bohr, P.H. Damgaard, G. Festuccia, L. Plant\u00e9 and P. Vanhove, General relativity from scattering amplitudes, Phys. Rev. Lett. 121 (2018) 171601 [arXiv:1806.04920] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"14774_CR86","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/JHEP02(2019)137","volume":"02","author":"DA Kosower","year":"2019","unstructured":"D.A. Kosower, B. Maybee and D. O\u2019Connell, Amplitudes, observables, and classical scattering, JHEP 02 (2019) 137 [arXiv:1811.10950] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR87","doi-asserted-by":"publisher","first-page":"251101","DOI":"10.1103\/PhysRevLett.121.251101","volume":"121","author":"C Cheung","year":"2018","unstructured":"C. Cheung, I.Z. Rothstein and M.P. Solon, From scattering amplitudes to classical potentials in the post-Minkowskian expansion, Phys. Rev. Lett. 121 (2018) 251101 [arXiv:1808.02489] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"14774_CR88","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.100.084040","volume":"100","author":"A Cristofoli","year":"2019","unstructured":"A. Cristofoli, N.E.J. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Post-Minkowskian Hamiltonians in general relativity, Phys. Rev. D 100 (2019) 084040 [arXiv:1906.01579] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR89","doi-asserted-by":"publisher","first-page":"201603","DOI":"10.1103\/PhysRevLett.122.201603","volume":"122","author":"Z Bern","year":"2019","unstructured":"Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M.P. Solon and M. Zeng, Scattering amplitudes and the conservative Hamiltonian for binary systems at third post-Minkowskian order, Phys. Rev. Lett. 122 (2019) 201603 [arXiv:1901.04424] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"14774_CR90","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1007\/JHEP10(2019)206","volume":"10","author":"Z Bern","year":"2019","unstructured":"Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M.P. Solon and M. Zeng, Black hole binary dynamics from the double copy and effective theory, JHEP 10 (2019) 206 [arXiv:1908.01493] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR91","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.91.024017","volume":"91","author":"V Vaidya","year":"2015","unstructured":"V. Vaidya, Gravitational spin Hamiltonians from the S matrix, Phys. Rev. D 91 (2015) 024017 [arXiv:1410.5348] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR92","doi-asserted-by":"publisher","first-page":"056","DOI":"10.1007\/JHEP09(2019)056","volume":"09","author":"A Guevara","year":"2019","unstructured":"A. Guevara, A. Ochirov and J. Vines, Scattering of spinning black holes from exponentiated soft factors, JHEP 09 (2019) 056 [arXiv:1812.06895] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR93","doi-asserted-by":"publisher","first-page":"104024","DOI":"10.1103\/PhysRevD.100.104024","volume":"100","author":"A Guevara","year":"2019","unstructured":"A. Guevara, A. Ochirov and J. Vines, Black-hole scattering with general spin directions from minimal-coupling amplitudes, Phys. Rev. D 100 (2019) 104024 [arXiv:1906.10071] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR94","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1007\/JHEP12(2019)156","volume":"12","author":"B Maybee","year":"2019","unstructured":"B. Maybee, D. O\u2019Connell and J. Vines, Observables and amplitudes for spinning particles and black holes, JHEP 12 (2019) 156 [arXiv:1906.09260] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR95","unstructured":"Z. Bern, A. Luna, R. Roiban, C.-H. Shen and M. Zeng, Spinning black hole binary dynamics, scattering amplitudes and effective field theory, arXiv:2005.03071 [INSPIRE]."},{"key":"14774_CR96","doi-asserted-by":"publisher","first-page":"070","DOI":"10.1007\/JHEP11(2019)070","volume":"11","author":"PH Damgaard","year":"2019","unstructured":"P.H. Damgaard, K. Haddad and A. Helset, Heavy black hole effective theory, JHEP 11 (2019) 070 [arXiv:1908.10308] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR97","doi-asserted-by":"publisher","first-page":"051","DOI":"10.1007\/JHEP05(2020)051","volume":"05","author":"R Aoude","year":"2020","unstructured":"R. Aoude, K. Haddad and A. Helset, On-shell heavy particle effective theories, JHEP 05 (2020) 051 [arXiv:2001.09164] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR98","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.102.024060","volume":"102","author":"T Damour","year":"2020","unstructured":"T. Damour, Classical and quantum scattering in post-Minkowskian gravity, Phys. Rev. D 102 (2020) 024060 [arXiv:1912.02139] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR99","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.97.044038","volume":"97","author":"T Damour","year":"2018","unstructured":"T. Damour, High-energy gravitational scattering and the general relativistic two-body problem, Phys. Rev. D 97 (2018) 044038 [arXiv:1710.10599] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR100","doi-asserted-by":"publisher","first-page":"072","DOI":"10.1007\/JHEP01(2020)072","volume":"01","author":"G K\u00e4lin","year":"2020","unstructured":"G. K\u00e4lin and R.A. Porto, From boundary data to bound states, JHEP 01 (2020) 072 [arXiv:1910.03008] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR101","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/JHEP02(2020)120","volume":"02","author":"G K\u00e4lin","year":"2020","unstructured":"G. K\u00e4lin and R.A. Porto, From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist), JHEP 02 (2020) 120 [arXiv:1911.09130] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR102","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1016\/S0370-2693(00)00978-3","volume":"490","author":"F Bastianelli","year":"2000","unstructured":"F. Bastianelli, O. Corradini and P. van Nieuwenhuizen, Dimensional regularization of the path integral in curved space on an infinite time interval, Phys. Lett. B 490 (2000) 154 [hep-th\/0007105] [INSPIRE].","journal-title":"Phys. Lett. B"},{"key":"14774_CR103","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1016\/S0550-3213(02)00683-1","volume":"642","author":"F Bastianelli","year":"2002","unstructured":"F. Bastianelli and A. Zirotti, Worldline formalism in a gravitational background, Nucl. Phys. B 642 (2002) 372 [hep-th\/0205182] [INSPIRE].","journal-title":"Nucl. Phys. B"},{"key":"14774_CR104","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/0550-3213(94)90361-1","volume":"419","author":"M Fabbrichesi","year":"1994","unstructured":"M. Fabbrichesi, R. Pettorino, G. Veneziano and G.A. Vilkovisky, Planckian energy scattering and surface terms in the gravitational action, Nucl. Phys. B 419 (1994) 147 [hep-th\/9309037] [INSPIRE].","journal-title":"Nucl. Phys. B"},{"key":"14774_CR105","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/0370-2693(89)91366-X","volume":"216","author":"D Amati","year":"1989","unstructured":"D. Amati, M. Ciafaloni and G. Veneziano, Can space-time be probed below the string size?, Phys. Lett. B 216 (1989) 41 [INSPIRE].","journal-title":"Phys. Lett. B"},{"key":"14774_CR106","doi-asserted-by":"publisher","first-page":"550","DOI":"10.1016\/0550-3213(90)90375-N","volume":"347","author":"D Amati","year":"1990","unstructured":"D. Amati, M. Ciafaloni and G. Veneziano, Higher order gravitational deflection and soft Bremsstrahlung in planckian energy superstring collisions, Nucl. Phys. B 347 (1990) 550 [INSPIRE].","journal-title":"Nucl. Phys. B"},{"key":"14774_CR107","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1103\/PhysRev.80.440","volume":"80","author":"RP Feynman","year":"1950","unstructured":"R.P. Feynman, Mathematical formulation of the quantum theory of electromagnetic interaction, Phys. Rev. 80 (1950) 440 [INSPIRE].","journal-title":"Phys. Rev."},{"key":"14774_CR108","volume-title":"Quantum field theory and the standard model","author":"MD Schwartz","year":"2014","unstructured":"M.D. Schwartz, Quantum field theory and the standard model, Cambridge University Press, Cambridge U.K. (2014)."},{"key":"14774_CR109","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/0550-3213(92)90098-V","volume":"385","author":"MJ Strassler","year":"1992","unstructured":"M.J. Strassler, Field theory without Feynman diagrams: one loop effective actions, Nucl. Phys. B 385 (1992) 145 [hep-ph\/9205205] [INSPIRE].","journal-title":"Nucl. Phys. B"},{"key":"14774_CR110","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1016\/0550-3213(92)90134-W","volume":"379","author":"Z Bern","year":"1992","unstructured":"Z. Bern and D.A. Kosower, The computation of loop amplitudes in gauge theories, Nucl. Phys. B 379 (1992) 451 [INSPIRE].","journal-title":"Nucl. Phys. B"},{"key":"14774_CR111","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/S0370-1573(01)00013-8","volume":"355","author":"C Schubert","year":"2001","unstructured":"C. Schubert, Perturbative quantum field theory in the string inspired formalism, Phys. Rept. 355 (2001) 73 [hep-th\/0101036] [INSPIRE].","journal-title":"Phys. Rept."},{"key":"14774_CR112","unstructured":"J.P. Edwards and C. Schubert, Quantum mechanical path integrals in the first quantised approach to quantum field theory, arXiv:1912.10004 [INSPIRE]."},{"key":"14774_CR113","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1103\/RevModPhys.29.377","volume":"29","author":"BS DeWitt","year":"1957","unstructured":"B.S. DeWitt, Dynamical theory in curved spaces. 1. A review of the classical and quantum action principles, Rev. Mod. Phys. 29 (1957) 377 [INSPIRE].","journal-title":"Rev. Mod. Phys."},{"key":"14774_CR114","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1103\/PhysRevD.19.438","volume":"19","author":"L Parker","year":"1979","unstructured":"L. Parker, Path integrals for a particle in curved space, Phys. Rev. D 19 (1979) 438 [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR115","doi-asserted-by":"publisher","first-page":"2850","DOI":"10.1103\/PhysRevD.23.2850","volume":"23","author":"JD Bekenstein","year":"1981","unstructured":"J.D. Bekenstein and L. Parker, Path integral evaluation of Feynman propagator in curved space-time, Phys. Rev. D 23 (1981) 2850 [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR116","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/0550-3213(93)90285-W","volume":"389","author":"F Bastianelli","year":"1993","unstructured":"F. Bastianelli and P. van Nieuwenhuizen, Trace anomalies from quantum mechanics, Nucl. Phys. B 389 (1993) 53 [hep-th\/9208059] [INSPIRE].","journal-title":"Nucl. Phys. B"},{"key":"14774_CR117","doi-asserted-by":"publisher","first-page":"114877","DOI":"10.1016\/j.nuclphysb.2019.114877","volume":"950","author":"N Ahmadiniaz","year":"2020","unstructured":"N. Ahmadiniaz, F.M. Balli, O. Corradini, J.M. D\u00e1vila and C. Schubert, Compton-like scattering of a scalar particle with N photons and one graviton, Nucl. Phys. B 950 (2020) 114877 [arXiv:1908.03425] [INSPIRE].","journal-title":"Nucl. Phys. B"},{"key":"14774_CR118","doi-asserted-by":"publisher","first-page":"4598","DOI":"10.1103\/PhysRevD.53.4598","volume":"53","author":"K Daikouji","year":"1996","unstructured":"K. Daikouji, M. Shino and Y. Sumino, Bern-Kosower rule for scalar QED, Phys. Rev. D 53 (1996) 4598 [hep-ph\/9508377] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR119","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.93.045023","volume":"93","author":"N Ahmadiniaz","year":"2016","unstructured":"N. Ahmadiniaz, A. Bashir and C. Schubert, Multiphoton amplitudes and generalized Landau-Khalatnikov-Fradkin transformation in scalar QED, Phys. Rev. D 93 (2016) 045023 [arXiv:1511.05087] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR120","doi-asserted-by":"crossref","unstructured":"N. Ahmadiniaz, F. Bastianelli and O. Corradini, Dressed scalar propagator in a non-Abelian background from the worldline formalism, Phys. Rev. D 93 (2016) 025035 [Addendum ibid. 93 (2016) 049904] [arXiv:1508.05144] [INSPIRE].","DOI":"10.1103\/PhysRevD.93.025035"},{"key":"14774_CR121","unstructured":"D. Bonocore, Asymptotic dynamics on the worldline for spinning particles, arXiv:2009.07863 [INSPIRE]."},{"key":"14774_CR122","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/0370-2693(87)90346-7","volume":"197","author":"D Amati","year":"1987","unstructured":"D. Amati, M. Ciafaloni and G. Veneziano, Superstring collisions at Planckian energies, Phys. Lett. B 197 (1987) 81 [INSPIRE].","journal-title":"Phys. Lett. B"},{"key":"14774_CR123","doi-asserted-by":"publisher","first-page":"124008","DOI":"10.1103\/PhysRevD.102.124008","volume":"102","author":"T Damour","year":"2020","unstructured":"T. Damour, Radiative contribution to classical gravitational scattering at the third order in G, Phys. Rev. D 102 (2020) 124008 [arXiv:2010.01641] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR124","doi-asserted-by":"publisher","first-page":"135924","DOI":"10.1016\/j.physletb.2020.135924","volume":"811","author":"P Di Vecchia","year":"2020","unstructured":"P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, Universality of ultra-relativistic gravitational scattering, Phys. Lett. B 811 (2020) 135924 [arXiv:2008.12743] [INSPIRE].","journal-title":"Phys. Lett. B"},{"key":"14774_CR125","doi-asserted-by":"publisher","first-page":"046","DOI":"10.1007\/JHEP01(2020)046","volume":"01","author":"N Arkani-Hamed","year":"2020","unstructured":"N. Arkani-Hamed, Y.-t. Huang and D. O\u2019Connell, Kerr black holes as elementary particles, JHEP 01 (2020) 046 [arXiv:1906.10100] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR126","doi-asserted-by":"publisher","first-page":"056","DOI":"10.1007\/JHEP12(2014)056","volume":"12","author":"R Monteiro","year":"2014","unstructured":"R. Monteiro, D. O\u2019Connell and C.D. White, Black holes and the double copy, JHEP 12 (2014) 056 [arXiv:1410.0239] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR127","doi-asserted-by":"publisher","first-page":"1542008","DOI":"10.1142\/S0218271815420080","volume":"24","author":"R Monteiro","year":"2015","unstructured":"R. Monteiro, D. O\u2019Connell and C.D. White, Gravity as a double copy of gauge theory: from amplitudes to black holes, Int. J. Mod. Phys. D 24 (2015) 1542008 [INSPIRE].","journal-title":"Int. J. Mod. Phys. D"},{"key":"14774_CR128","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1016\/j.physletb.2015.09.021","volume":"750","author":"A Luna","year":"2015","unstructured":"A. Luna, R. Monteiro, D. O\u2019Connell and C.D. White, The classical double copy for Taub-NUT spacetime, Phys. Lett. B 750 (2015) 272 [arXiv:1507.01869] [INSPIRE].","journal-title":"Phys. Lett. B"},{"key":"14774_CR129","doi-asserted-by":"publisher","first-page":"125010","DOI":"10.1103\/PhysRevD.95.125010","volume":"95","author":"WD Goldberger","year":"2017","unstructured":"W.D. Goldberger and A.K. Ridgway, Radiation and the classical double copy for color charges, Phys. Rev. D 95 (2017) 125010 [arXiv:1611.03493] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR130","doi-asserted-by":"publisher","first-page":"124027","DOI":"10.1103\/PhysRevD.79.124027","volume":"79","author":"CR Galley","year":"2009","unstructured":"C.R. Galley and M. Tiglio, Radiation reaction and gravitational waves in the effective field theory approach, Phys. Rev. D 79 (2009) 124027 [arXiv:0903.1122] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR131","doi-asserted-by":"publisher","first-page":"174301","DOI":"10.1103\/PhysRevLett.110.174301","volume":"110","author":"CR Galley","year":"2013","unstructured":"C.R. Galley, Classical mechanics of nonconservative systems, Phys. Rev. Lett. 110 (2013) 174301 [arXiv:1210.2745] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"14774_CR132","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/JHEP06(2020)153","volume":"06","author":"AP Saha","year":"2020","unstructured":"A.P. Saha, B. Sahoo and A. Sen, Proof of the classical soft graviton theorem in D = 4, JHEP 06 (2020) 153 [arXiv:1912.06413] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR133","doi-asserted-by":"publisher","first-page":"070","DOI":"10.1007\/JHEP12(2020)070","volume":"12","author":"B Sahoo","year":"2020","unstructured":"B. Sahoo, Classical sub-subleading soft photon and soft graviton theorems in four spacetime dimensions, JHEP 12 (2020) 070 [arXiv:2008.04376] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR134","doi-asserted-by":"publisher","first-page":"086","DOI":"10.1007\/JHEP02(2019)086","volume":"02","author":"B Sahoo","year":"2019","unstructured":"B. Sahoo and A. Sen, Classical and quantum results on logarithmic terms in the soft theorem in four dimensions, JHEP 02 (2019) 086 [arXiv:1808.03288] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR135","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1007\/JHEP11(2018)162","volume":"11","author":"C-H Shen","year":"2018","unstructured":"C.-H. Shen, Gravitational radiation from color-kinematics duality, JHEP 11 (2018) 162 [arXiv:1806.07388] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR136","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1016\/j.cpc.2008.05.009","volume":"179","author":"JM Mart\u00edn-Garc\u00eda","year":"2008","unstructured":"J. M. Mart\u00edn-Garc\u00eda, xPerm: fast index canonicalization for tensor computer algebra, Comp. Phys. Commun. 179 (2008) 597 [arXiv:0803.0862].","journal-title":"Comp. Phys. Commun."},{"key":"14774_CR137","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/JHEP03(2020)173","volume":"03","author":"P Di Vecchia","year":"2020","unstructured":"P. Di Vecchia, S.G. Naculich, R. Russo, G. Veneziano and C.D. White, A tale of two exponentiations in $$ \\mathcal{N} $$ = 8 supergravity at subleading level, JHEP 03 (2020) 173 [arXiv:1911.11716] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR138","doi-asserted-by":"publisher","first-page":"124024","DOI":"10.1103\/PhysRevD.102.124024","volume":"102","author":"A Antonelli","year":"2020","unstructured":"A. Antonelli, C. Kavanagh, M. Khalil, J. Steinhoff and J. Vines, Gravitational spin-orbit and aligned spin1-spin2 couplings through third-subleading post-Newtonian orders, Phys. Rev. D 102 (2020) 124024 [arXiv:2010.02018] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR139","doi-asserted-by":"publisher","first-page":"023","DOI":"10.1007\/JHEP11(2020)023","volume":"11","author":"J Parra-Martinez","year":"2020","unstructured":"J. Parra-Martinez, M.S. Ruf and M. Zeng, Extremal black hole scattering at $$ \\mathcal{O}\\left({G}^3\\right) $$: graviton dominance, eikonal exponentiation, and differential equations, JHEP 11 (2020) 023 [arXiv:2005.04236] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR140","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.99.064054","volume":"99","author":"J Vines","year":"2019","unstructured":"J. Vines, J. Steinhoff and A. Buonanno, Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order, Phys. Rev. D 99 (2019) 064054 [arXiv:1812.00956] [INSPIRE].","journal-title":"Phys. Rev. D"},{"key":"14774_CR141","doi-asserted-by":"publisher","first-page":"759","DOI":"10.1016\/0550-3213(88)90442-7","volume":"306","author":"FA Berends","year":"1988","unstructured":"F.A. Berends and W.T. Giele, Recursive calculations for processes with n gluons, Nucl. Phys. B 306 (1988) 759 [INSPIRE].","journal-title":"Nucl. Phys. B"},{"key":"14774_CR142","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1007\/JHEP11(2019)124","volume":"11","author":"F Bastianelli","year":"2019","unstructured":"F. Bastianelli, R. Bonezzi, O. Corradini and E. Latini, One-loop quantum gravity from the $$ \\mathcal{N} $$ = 4 spinning particle, JHEP 11 (2019) 124 [arXiv:1909.05750] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR143","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/JHEP06(2020)103","volume":"06","author":"R Bonezzi","year":"2020","unstructured":"R. Bonezzi, A. Meyer and I. Sachs, A Worldline Theory for Supergravity, JHEP 06 (2020) 103 [arXiv:2004.06129] [INSPIRE].","journal-title":"JHEP"},{"key":"14774_CR144","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.100.086006","volume":"100","author":"J Plefka","year":"2019","unstructured":"J. Plefka, C. Shi, J. Steinhoff and T. Wang, Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO, Phys. Rev. D 100 (2019) 086006 [arXiv:1906.05875] [INSPIRE].","journal-title":"Phys. Rev. D"}],"container-title":["Journal of High Energy Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/JHEP02(2021)048.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/JHEP02(2021)048\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/JHEP02(2021)048.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,29]],"date-time":"2023-01-29T01:30:07Z","timestamp":1674955807000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/JHEP02(2021)048"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,5]]},"references-count":144,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["14774"],"URL":"https:\/\/doi.org\/10.1007\/jhep02(2021)048","relation":{},"ISSN":["1029-8479"],"issn-type":[{"value":"1029-8479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,5]]},"assertion":[{"value":"30 October 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 December 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 February 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"48"}}