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 h μν (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 〈h μv (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.
{ "_oai": { "updated": "2021-05-27T00:33:47Z", "id": "oai:repo.scoap3.org:59941", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "Sweden", "value": "Department of Physics and Astronomy, Uppsala University, Box 516, Uppsala, 75108, Sweden", "organization": "Uppsala University" }, { "country": "Germany", "value": "Institut f\u00fcr Physik und IRIS Adlershof, Humboldt-Universit\u00e4t zu Berlin, Zum Gro\u00dfen Windkanal 6, Berlin, D-12489, Germany", "organization": "Humboldt-Universit\u00e4t zu Berlin" }, { "country": "Germany", "value": "Max-Planck-Institut f\u00fcr Gravitationsphysik (Albert-Einstein-Institut), M\u00fchlenberg 1, Potsdam, D-14476, Germany", "organization": "Max-Planck-Institut f\u00fcr Gravitationsphysik (Albert-Einstein-Institut)" } ], "surname": "Mogull", "email": "gustav.mogull@aei.mpg.de", "full_name": "Mogull, Gustav", "given_names": "Gustav" }, { "affiliations": [ { "country": "Germany", "value": "Institut f\u00fcr Physik und IRIS Adlershof, Humboldt-Universit\u00e4t zu Berlin, Zum Gro\u00dfen Windkanal 6, Berlin, D-12489, Germany", "organization": "Humboldt-Universit\u00e4t zu Berlin" } ], "surname": "Plefka", "email": "jan.plefka@hu-berlin.de", "full_name": "Plefka, Jan", "given_names": "Jan" }, { "affiliations": [ { "country": "Germany", "value": "Max-Planck-Institut f\u00fcr Gravitationsphysik (Albert-Einstein-Institut), M\u00fchlenberg 1, Potsdam, D-14476, Germany", "organization": "Max-Planck-Institut f\u00fcr Gravitationsphysik (Albert-Einstein-Institut)" } ], "surname": "Steinhoff", "email": "jan.steinhoff@aei.mpg.de", "full_name": "Steinhoff, Jan", "given_names": "Jan" } ], "titles": [ { "source": "Springer", "title": "Classical black hole scattering from a worldline quantum field theory" } ], "dois": [ { "value": "10.1007/JHEP02(2021)048" } ], "publication_info": [ { "page_end": "43", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2021", "artid": "JHEP02(2021)048", "year": 2021, "page_start": "1", "journal_issue": "2" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2021-05-27T00:30:41.800637", "source": "Springer", "method": "Springer", "submission_number": "abbf0a02be8211eb92440a580a640a05" }, "page_nr": [ 43 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2021" } ], "control_number": "59941", "record_creation_date": "2021-02-05T22:30:22.029744", "_files": [ { "checksum": "md5:34e15142a48b88916258ec2e017b8336", "filetype": "xml", "bucket": "f19d0133-5b09-47fa-aea2-810b293163f9", "version_id": "e38ea8bc-8fc8-4320-9674-0349fa2db4da", "key": "10.1007/JHEP02(2021)048.xml", "size": 14789 }, { "checksum": "md5:1211f822d2ffb13a9b5b0a982db29053", "filetype": "pdf/a", "bucket": "f19d0133-5b09-47fa-aea2-810b293163f9", "version_id": "9da7c5f6-2485-4509-abe7-b0d098d8a895", "key": "10.1007/JHEP02(2021)048_a.pdf", "size": 816492 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "gr-qc" ], "value": "2010.02865" } ], "abstracts": [ { "source": "Springer", "value": "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 h \u03bc\u03bd (x) and position <math> <msubsup> <mi>x</mi> <mi>i</mi> <mi>\u03bc</mi> </msubsup> <mfenced> <msub> <mi>\u03c4</mi> <mi>i</mi> </msub> </mfenced> </math> $$ {x}_i^{\\mu}\\left({\\tau}_i\\right) $$ of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation \u2329h \u03bcv (k)\u232a and 2PM two-body deflection <math> <mi>\u0394</mi> <msubsup> <mi>p</mi> <mi>i</mi> <mi>\u03bc</mi> </msubsup> </math> $$ \\Delta {p}_i^{\\mu } $$ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 \u2192 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT." } ], "imprints": [ { "date": "2021-02-05", "publisher": "Springer" } ] }