Canonical realizations of Bondi-Metzner-Sachs–like symmetries in field theory
(English) The BMS group appears as an infinite-dimensional group of isometries of asymptotically flat spacetimes first introduced by Bondi, Metzner, van der Burg, and Sachs in 1962. This group has gained interest recently due to the invariance of the gravitational S-matrix under these transformation...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/692312 |
| Acceso en línea: | http://hdl.handle.net/10803/692312 https://dx.doi.org/10.5821/dissertation-2117-416264 |
| Access Level: | acceso abierto |
| Palabra clave: | Àrees temàtiques de la UPC::Matemàtiques i estadística 512 |
| Sumario: | (English) The BMS group appears as an infinite-dimensional group of isometries of asymptotically flat spacetimes first introduced by Bondi, Metzner, van der Burg, and Sachs in 1962. This group has gained interest recently due to the invariance of the gravitational S-matrix under these transformations and the existence of a connection between Weinberg's soft gravitons theorems and Ward identities of BMS supertranslations, and also due to the relation between flat space holography and BMS. Despite being originally related to gravitational physics, the BMS group and its Lie algebra can be realized in free flat field theories by means of the Fourier modes of the field. One of these realizations, which we refer to as the canonical realization, can be built for a free scalar field in Minkowski space using a generalization of the usual Poincar\'e charges. In this Thesis, we study in detail the canonical realization to uncover the expression of the infinite-dimensional conserved charges associated with BMS transformations in d=3 spacetime. The final expression consists of an integral transformation in terms of derivatives of polyharmonic Green functions. We later explore a particle non-linear realization of BMS using the Maurer-Cartan form to find an infinite set of BMS coordinates that are constrained by gauge transformations. We construct the corresponding Poincaré transformation generators in terms of these infinite-dimensional coordinates and the associated momenta. Finally, we study the extension of BMS with conformal transformations in the massless theory. We conclude that it is possible to extend the algebra to a Weyl-BMS realization by defining new superdilatation operators, but the incorporation of special conformal transformations results in an infinite tower of new operators that need further study. The work presented in this Thesis could be of some use for the study of flat-space holography since it describes a field theory in three-dimensional space-time that could act as the dual to asymptotic flat gravity theory in the bulk. |
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