Quantum gravitational corrections to the nonrelativistic scattering potential of two masses

By N. Bjerrum-Bohr, John Donoghue, B. Holstein. 2002

355 citations recorded by the source corpus.

We treat general relativity as an effective field theory, obtaining the full nonanalytic component of the scattering matrix potential to one-loop order. The lowest order vertex rules for the resulting effective field theory are presented and the one-loop diagrams which yield the leading nonrelativistic post-Newtonian and quantum corrections to the gravitational scattering amplitude to second order in G are calculated in detail. The Fourier transformed amplitudes yield a nonrelativistic potential and our result is discussed in relation to previous calculations. The definition of a potential is discussed as well, and we show that the ambiguity of the potential under coordinate changes is resolved.

View Paper: https://www.semanticscholar.org/paper/5b53cb3dba1750e1618e1d4daa842a84bb7561fa

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1. T. Damour
2. A. Guevara
3. Ben Maybee
4. Rafael Aoude
5. Z. Bern
6. N. Bjerrum-Bohr
7. J. Vines
8. M. Niedermaier

Citations in the corpus

• The asymptotic safety scenario in quantum gravity: an introduction (2006, methodology): “The coefficient ζscatt was computed initially by Donoghue and later by Khriplovich–Kirilin; the result considered definite in [27] is ζscatt = 41 10π .”
• The Asymptotic Safety Scenario in Quantum Gravity (2006, methodology): “A number of authors have argued in the effective field theory framework that even theories with an infinite number of relevant parameters can be predictive [126, 16, 32].”
• Post-Minkowskian Hamiltonians in general relativity (2019, background): “[21, 22]), although most focus until now seems to have been on considering the quantum mechanical effects.”
• Tabletop experiments for quantum gravity: a user’s manual (2018, methodology): “As a concrete example of this approach, one can explicitly compute the leading quantum corrections to the Newtonian potential [48, 49].”
• Observables and amplitudes for spinning particles and black holes (2019, background): “classical and quantum corrections to gravitational potentials [38–51], and there has been significant recent progress in obtaining such corrections in the PM approximation [52–57].”
• The amplitude for classical gravitational scattering at third Post-Minkowskian order (2021, background): “(3)We note that the static limit of the second line matches the quantum correction to the one-loop amplitude evaluated in [35, 36]”
• On-shell techniques and universal results in quantum gravity (2013, methodology): “which provides a useful gauge invariant amplitude with which to display the quantum corrections [8].”
• On-shell heavy particle effective theories (2020, methodology): “Indeed, the effective field theory (EFT) of GR [2, 3] has been used extensively to compute classical corrections to the gravitational potential [3–11].”
• Holomorphic classical limit for spin effects in gravitational and electromagnetic scattering (2017, methodology): “in agreement with the computations in [20, 59, 67, 72].”
• Quantum-Spacetime Phenomenology (2008, background): “And one does derive a correction to Newton’s potential with behavior [210, 27, 329, 120, 324, 449]”
• Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory (2003, background): “A number of these calculations have now been performed [82, 93, 83, 86, 102, 103, 90], and it is the results of [57, 56, 21, 20] which are summarized here.”