A Celestial Kinematical Interpretation for an Extended BMS$_4$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915502010400768 |
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| author | Batlle, Carles Casalbuoni, Roberto Dominici, Daniele Figueroa-O'Farrill, José Gomis, Joaquim |
| author_facet | Batlle, Carles Casalbuoni, Roberto Dominici, Daniele Figueroa-O'Farrill, José Gomis, Joaquim |
| contents | 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 Poincaré 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_00957 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Celestial Kinematical Interpretation for an Extended BMS$_4$ Batlle, Carles Casalbuoni, Roberto Dominici, Daniele Figueroa-O'Farrill, José Gomis, Joaquim High Energy Physics - Theory 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 Poincaré 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. |
| title | A Celestial Kinematical Interpretation for an Extended BMS$_4$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.00957 |