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Journal Article

A free Lie algebra approach to curvature corrections to flat space-time


Kleinschmidt,  Axel
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Gomis, J., Kleinschmidt, A., Roest, D., & Salgado-Rebolledo, P. (2020). A free Lie algebra approach to curvature corrections to flat space-time. Journal of High Energy Physics, 2020(9): 68. doi:10.1007/JHEP09(2020)068.

Cite as: https://hdl.handle.net/21.11116/0000-0006-99E6-A
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${}_\infty$, 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.