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arXiv · 2506.00957

A Celestial Kinematical Interpretation for an Extended BMS$_4$

Carles Batlle·Roberto Casalbuoni·Daniele Dominici·José Figueroa-O'Farrill·Joaquim Gomis
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Abstract

Motivated by the work of Longhi and Materassi, who constructed a realisation of the (centreless) BMS$_4$ algebra for the massive Klein-Gordon field in $3+1$, we build a realisation of the (centreless) massless BMS$_4$ 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$_4$ algebra in terms of vector fields shows its kinematical nature, like the Poincar\'e algebra. We also construct a dynamical realisation of BMS$_4$ 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$_4$ 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.

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Carles Batlle, Roberto Casalbuoni, Daniele Dominici, José Figueroa-O'Farrill, Joaquim Gomis. 2025-06-01. A Celestial Kinematical Interpretation for an Extended BMS$_4$. https://arxiv.org/abs/2506.00957

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