Year: 2025
Type: article
Abstract: Motivated by the work of Longhi and Materassi, who constructed a realization of the (centerless) BMS 4 algebra for the massive Klein-Gordon field in 3 + 1 dimensions, we build a realization of the (centerless) massless BMS 4 algebra including superrotations. This realization depends only on the momenta in the light cone 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 realization 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.
DOI: 10.1103/8j34-cg6d
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Awards: G1175115578, G1545928676, G1923596229, G2064873908, G210041235, G2262748287, G2601397997, G288263039, G2981624247, G3005324705, G300979063, G3089118260, G34346518, G3480869486, G3681454997, G3774114341, G3780874795, G3978510197, G4042783231, G410571670, G4249909660, G425668148, G451917667, G5080475149, G5338730000, G5852091828, G5915139351, G5967599077, G6816770786, G716185866, G8607709445
OpenAlex ID: W4417045302