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 Poincar\'e 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 Poincar\'e, 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.
Keywords
Cite
@article{arxiv.2006.11102,
title = {A free Lie algebra approach to curvature corrections to flat space-time},
author = {Joaquim Gomis and Axel Kleinschmidt and Diederik Roest and Patricio Salgado-Rebolledo},
journal= {arXiv preprint arXiv:2006.11102},
year = {2020}
}
Comments
23 pages