Amplitudes for astrophysicists: known knowns

  • Daniel J. Burger
  • Raúl Carballo-Rubio
  • Nathan MoynihanEmail author
  • Jeff Murugan
  • Amanda Weltman
Research Article


The use of quantum field theory to understand astrophysical phenomena is not new. However, for the most part, the methods used are those that have been developed decades ago. The intervening years have seen some remarkable developments in computational quantum field theoretic tools. In particle physics, this technology has facilitated calculations that, even ten years ago would have seemed laughably difficult. It is remarkable, then, that most of these new techniques have remained firmly within the domain of high energy physics. We would like to change this. As alluded to in the title, this paper is aimed at showcasing the use of modern on-shell methods in the context of astrophysics and cosmology. In this article, we use the old problem of the bending of light by a compact object as an anchor to pedagogically develop these new computational tools. Once developed, we then illustrate their power and utility with an application to the scattering of gravitational waves.


Scattering amplitudes Astrophysics Light bending Gravitational waves Quantum field theory S matrix 



We would like to thank Timothy Adamo, Daniel Grin, Malcolm Perry and Edward Witten for useful discussions. RCR is funded by a postdoctoral fellowship from the Claude Leon Foundation of South Africa. DB is supported by a PHD fellowship from the South African National Institute for Theoretical Physics (NITheP). JM gratefully acknowledges support by NSF Grant PHY-1606531 at the Institute for Advanced Study and NRF Grant GUN 87667 at the University of Cape Town. AW would like to thank the Institute for Advanced study, the Simons Foundation and the Flatiron Institute where part of this work was completed, as well as the Princeton University Astrophysics department for their generous support. AW and NM are supported by the South African Research Chairs Initiative of the Department of Science and Technology and the National Research Foundation of South Africa. Any opinion, finding and conclusion or recommendation expressed in this material is that of the authors and the NRF does not accept any liability in this regard. Finally, JM and AW would like to thank Carl Feinberg for his generous support of the accumulation of useless knowledge at the Institute for Advanced Study.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Daniel J. Burger
    • 1
    • 2
  • Raúl Carballo-Rubio
    • 1
    • 2
    • 3
    • 4
  • Nathan Moynihan
    • 1
    • 2
  • Jeff Murugan
    • 1
    • 5
  • Amanda Weltman
    • 2
    • 5
    • 6
  1. 1.The Laboratory for Quantum Gravity and StringsUniversity of Cape TownRondeboschSouth Africa
  2. 2.The Cosmology and Gravity Group, Department of Mathematics and Applied MathematicsUniversity of Cape TownRondeboschSouth Africa
  3. 3.SISSA, International School for Advanced StudiesTriesteItaly
  4. 4.INFN Sezione di TriesteTriesteItaly
  5. 5.School of Natural SciencesInstitute for Advanced StudyPrincetonUSA
  6. 6.Department of Astrophysical Sciences, Peyton HallPrinceton UniversityPrincetonUSA

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