A free Lie algebra approach to curvature corrections to flat space-time
Abstract We investigate a systematic approach to include curvature corrections to the isometry algebra of flat space-time order-by-order in the curvature scale. The Poincaré algebra is extended to a free Lie algebra, with generalised boosts and translations that no longer commute. The additional gen...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP09(2020)068 |
| _version_ | 1818623240950513664 |
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| author | Joaquim Gomis Axel Kleinschmidt Diederik Roest Patricio Salgado-Rebolledo |
| author_facet | Joaquim Gomis Axel Kleinschmidt Diederik Roest Patricio Salgado-Rebolledo |
| author_sort | Joaquim Gomis |
| collection | DOAJ |
| description | Abstract We investigate a systematic approach to include curvature corrections to the isometry algebra of flat space-time order-by-order in the curvature scale. The Poincaré algebra is extended to a free Lie algebra, with generalised boosts and translations that no longer commute. The additional generators satisfy a level-ordering and encode the curvature corrections at that order. This eventually results in an infinite-dimensional algebra that we refer to as Poincaré∞, and we show that it contains among others an (A)dS quotient. We discuss a non-linear realisation of this infinite-dimensional algebra, and construct a particle action based on it. The latter yields a geodesic equation that includes (A)dS curvature corrections at every order. |
| first_indexed | 2024-12-16T18:37:56Z |
| format | Article |
| id | doaj.art-f012ee4d81d440e8acc61c80bb04f8f5 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-16T18:37:56Z |
| publishDate | 2020-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-f012ee4d81d440e8acc61c80bb04f8f52022-12-21T22:21:08ZengSpringerOpenJournal of High Energy Physics1029-84792020-09-012020912310.1007/JHEP09(2020)068A free Lie algebra approach to curvature corrections to flat space-timeJoaquim Gomis0Axel Kleinschmidt1Diederik Roest2Patricio Salgado-Rebolledo3Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Universitat de BarcelonaMax-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)Van Swinderen Institute for Particle Physics and Gravity, University of GroningenSchool of Physics and Astronomy, University of LeedsAbstract We investigate a systematic approach to include curvature corrections to the isometry algebra of flat space-time order-by-order in the curvature scale. The Poincaré algebra is extended to a free Lie algebra, with generalised boosts and translations that no longer commute. The additional generators satisfy a level-ordering and encode the curvature corrections at that order. This eventually results in an infinite-dimensional algebra that we refer to as Poincaré∞, and we show that it contains among others an (A)dS quotient. We discuss a non-linear realisation of this infinite-dimensional algebra, and construct a particle action based on it. The latter yields a geodesic equation that includes (A)dS curvature corrections at every order.http://link.springer.com/article/10.1007/JHEP09(2020)068Global SymmetriesSpace-Time SymmetriesClassical Theories of Gravity |
| spellingShingle | Joaquim Gomis Axel Kleinschmidt Diederik Roest Patricio Salgado-Rebolledo A free Lie algebra approach to curvature corrections to flat space-time Journal of High Energy Physics Global Symmetries Space-Time Symmetries Classical Theories of Gravity |
| title | A free Lie algebra approach to curvature corrections to flat space-time |
| title_full | A free Lie algebra approach to curvature corrections to flat space-time |
| title_fullStr | A free Lie algebra approach to curvature corrections to flat space-time |
| title_full_unstemmed | A free Lie algebra approach to curvature corrections to flat space-time |
| title_short | A free Lie algebra approach to curvature corrections to flat space-time |
| title_sort | free lie algebra approach to curvature corrections to flat space time |
| topic | Global Symmetries Space-Time Symmetries Classical Theories of Gravity |
| url | http://link.springer.com/article/10.1007/JHEP09(2020)068 |
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