A Celestial Kinematical Interpretation for an Extended BMS$_4$
Abstract
Motivated by the work of Longhi and Materassi, who constructed a realisation of the (centreless) BMS algebra for the massive Klein-Gordon field in , we build a realisation of the (centreless) massless BMS algebra including super-rotations. This realisation depends only on the momenta in the lightcone expressed in celestial coordinates without any reference to the Klein--Gordon field. The quadratic Casimir of the Lorentz algebra is written in terms of a second order differential operator and the volume form plays an essential role in this construction. The BMS algebra in terms of vector fields shows its kinematical nature, like the Poincar\'e algebra. We also construct a dynamical realisation of BMS from the symplectic structure on the solutions of the massless four-dimensional Klein--Gordon field in terms of quadratic expressions of the Fourier modes and plane waves invariant under translations. Using the Mellin transform, we rewrite the Klein--Gordon field in terms of the boost invariant basis, and write down the corresponding BMS realization. We also provide the relation with spherical harmonics, linking our results with the solutions of Longhi-Materassi, which are in fact a subset of ours.
Keywords
Cite
@article{arxiv.2506.00957,
title = {A Celestial Kinematical Interpretation for an Extended BMS$_4$},
author = {Carles Batlle and Roberto Casalbuoni and Daniele Dominici and José Figueroa-O'Farrill and Joaquim Gomis},
journal= {arXiv preprint arXiv:2506.00957},
year = {2025}
}
Comments
Enlarged version. Two new sections about the scalar field realization in the boost basis, using the Mellin transform, and the relation to the Longhi-Materassi construction in terms of spherical harmonics have been added, as well as a short discussion about the massive case and a new appendix. Minor typos have been corrected and new references have been included. JG has updated his affiliation