- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Bondi-Metzner-Sachs Particles

Xavier Bekaert1,*, Laura Donnay2,†, and Yannick Herfray1,‡

  • *Contact author: xavier.bekaert@univ-tours.fr
  • †Contact author: ldonnay@sissa.it
  • ‡Contact author: yannick.herfray@univ-tours.fr
PDF

Phys. Rev. Lett. 135, 131602 – Published 23 September, 2025

DOI: https://doi.org/10.1103/8376-fync

Abstract

We construct wave functions for unitary irreducible representations (UIRs) of the Bondi-Metzner-Sachs (BMS) group, i.e., BMS particles, and show that they describe quantum superpositions of (Poincaré) particles propagating on inequivalent gravity vacua. This follows from reconsidering McCarthy’s classification of BMS group UIRs through a unique, Lorentz-invariant, but nonlinear, decomposition of supermomenta into hard and soft pieces.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (54)

  1. H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. R. Soc. A 269, 21 (1962).
  2. R. Sachs, Gravitational waves in general relativity. VI. The outgoing radiation condition, Proc. R. Soc. A 264, 309 (1961).
  3. R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128, 2851 (1962).
  4. A. Strominger, On BMS invariance of gravitational scattering, J. High Energy Phys. 07 (2014) 152.
  5. T. He, V. Lysov, P. Mitra, and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, J. High Energy Phys. 05 (2015) 151.
  6. A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory (Princeton University Press, Princeton, NJ, 2018).
  7. N. F. Mott, On the influence of radiative forces on the scattering of electrons, Math. Proc. Cambridge Philos. Soc. 27, 255 (1931).
  8. A. Sommerfeld, Über die Beugung und Bremsung der Elektronen, Ann. Phys. (Berlin) 403, 257 (1931).
  9. F. Bloch and A. Nordsieck, Note on the radiation field of the electron, Phys. Rev. 52, 54 (1937).
  10. D. Kapec, M. Perry, A.-M. Raclariu, and A. Strominger, Infrared divergences in QED, revisited, Phys. Rev. D 96, 085002 (2017).
  11. B. Gabai and A. Sever, Large gauge symmetries and asymptotic states in QED, J. High Energy Phys. 12 (2016) 095.
  12. S. Choi and R. Akhoury, BMS supertranslation symmetry implies Faddeev-Kulish amplitudes, J. High Energy Phys. 02 (2018) 171.
  13. G. Arcioni and C. Dappiaggi, Holography in asymptotically flat space-times and the BMS group, Classical Quantum Gravity 21, 5655 (2004).
  14. G. Arcioni and C. Dappiaggi, Exploring the holographic principle in asymptotically flat space-times via the BMS group, Nucl. Phys. B674, 553 (2003).
  15. C. Dappiaggi, BMS field theory and holography in asymptotically flat space-times, J. High Energy Phys. 11 (2004) 011.
  16. C. Dappiaggi, V. Moretti, and N. Pinamonti, Rigorous steps towards holography in asymptotically flat spacetimes, Rev. Math. Phys. 18, 349 (2006).
  17. P. J. M. McCarthy, Asymptotically flat space-times and elementary particles, Phys. Rev. Lett. 29, 817 (1972).
  18. P. J. McCarthy, Representations of the Bondi-Metzner-Sachs group. I. Determination of the representations, Proc. R. Soc. A 330, 517 (1972).
  19. P. J. McCarthy, Representations of the Bondi-Metzner-Sachs group. II. Properties and classification of the representations, Proc. R. Soc. A 333, 317 (1973).
  20. P. J. McCarthy and M. Crampin, Representations of the Bondi-Metzner-Sachs group. III. Poincare spin multiplicities and irreducibility, Proc. R. Soc. A 335, 301 (1973).
  21. P. J. McCarthy, The Bondi-Metzner-Sachs group in the nuclear topology, Proc. R. Soc. A 343, 489 (1975).
  22. M. Crampin and P. J. McCarthy, Representations of the Bondi-Metzner-Sachs group. IV. Cantoni representations are induced, Proc. R. Soc. A 351, 55 (1976).
  23. P. J. McCarthy, Lifting of projective representations of the Bondi–Metzner–Sachs group, Proc. R. Soc. A 358, 141 (1978).
  24. P. J. McCarthy, Hyperfunctions and asymptotic symmetries, Proc. R. Soc. A 358, 495 (1978).
  25. V. Cantoni, A class of representations of the generalized Bondi–Metzner group, J. Math. Phys. (N.Y.) 7, 1361 (1966).
  26. V. Cantoni, Reduction of some representations of the generalized Bondi–Metzner group, J. Math. Phys. (N.Y.) 8, 1700 (1967).
  27. L. Girardello and G. Parravicini, Continuous spins in the Bondi-Metzner-Sachs group of asymptotic symmetry in general relativity, Phys. Rev. Lett. 32, 565 (1974).
  28. G. Barnich and B. Oblak, Notes on the BMS group in three dimensions: I. Induced representations, J. High Energy Phys. 06 (2014) 129.
  29. G. Barnich and B. Oblak, Notes on the BMS group in three dimensions: II. Coadjoint representation, J. High Energy Phys. 03 (2015) 033.
  30. B. Oblak, BMS particles in three dimensions, Ph.D. thesis, University of Brussels, 2016.
  31. R. K. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128, 2851 (1962).
  32. G. Longhi and M. Materassi, A canonical realization of the BMS algebra, J. Math. Phys. (N.Y.) 40, 480 (1999).
  33. A. Ashtekar, Asymptotic Quantization: Based on 1984 Naples Lectures (Bibliopolis, Naples, Italy, 1987).
  34. X. Bekaert and Y. Herfray, BMS representations for generic supermomentum, arXiv:2505.05368.
  35. A. Ashtekar, Geometry and physics of null infinity, Surv. Differ. Geom. 20, 99 (2015).
  36. E. T. Newman, Heaven and its properties, Gen. Relativ. Gravit. 7, 107 (1976).

  37. From the perspective of Newman’s H-space theory, we are here only dealing with the trivial case where spacetime is flat. In particular, the solutions are real.

  38. R. Penrose, Null hypersurface initial data for classical fields of arbitrary spin and for general relativity, Gen. Relativ. Gravit. 12, 225 (1980).
  39. R. Penrose and W. Rindler, Spinors and Space-Time (Cambridge University Press, Cambridge, England, 2011).
  40. E. Himwich, S. A. Narayanan, M. Pate, N. Paul, and A. Strominger, The soft S-matrix in gravity, J. High Energy Phys. 09 (2020) 129.

  41. The norm of the state is then given by a similar integral, see [34] for explicit realizations.

  42. L. Donnay and R. Ruzziconi, BMS flux algebra in celestial holography, J. High Energy Phys. 11 (2021) 040.
  43. G. Barnich and R. Ruzziconi, Coadjoint representation of the BMS group on celestial Riemann surfaces, J. High Energy Phys. 06 (2021) 079.

  44. Notice that this expression should not be understood as the action of a supermomentum creation operator and that the vacuum used here should not be confused with the zero-particle state of a Fock representation.

  45. The asymptotic group of QED is the semidirect product SO(3,1)⋉(R3,1⊕E[0]).

  46. D. Kapec and P. Mitra, Shadows and soft exchange in celestial CFT, Phys. Rev. D 105, 026009 (2022).
  47. D. Kapec, Y. T. A. Law, and S. A. Narayanan, Soft scalars and the geometry of the space of celestial CFTs, Phys. Rev. D 107, 046024 (2022).
  48. D. Kapec, Soft particles and infinite-dimensional geometry, Classical Quantum Gravity 41, 015001 (2024).
  49. P. P. Kulish and L. D. Faddeev, Asymptotic conditions and infrared divergences in quantum electrodynamics, Theor. Math. Phys. 4, 745 (1970).
  50. A. Chatterjee and D. A. Lowe, BMS symmetry, soft particles and memory, Classical Quantum Gravity 35, 094001 (2018).
  51. See Supplemental Material at http://link.aps.org/supplemental/10.1103/8376-fync for a more detailed discussion of the relationship between BMS states and the revisited Faddeev-Kulish states considered in Refs. [10,12].
  52. K. Prabhu, G. Satishchandran, and R. M. Wald, Infrared finite scattering theory in quantum field theory and quantum gravity, Phys. Rev. D 106, 066005 (2022).
  53. K. Prabhu and G. Satishchandran, Infrared finite scattering theory: Scattering states and representations of the BMS group, J. High Energy Phys. 08 (2024) 055.
  54. K. Prabhu and G. Satishchandran, Infrared finite scattering theory: Amplitudes and soft theorems, Phys. Rev. D 110, 085022 (2024).

Outline

Information

Phys. Rev. Lett. 135, 131602– Published 23 September, 2025
  • Received 17 May 2025
  • Accepted 28 August 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation