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.
Highlights
Such corrections to Poincare isometries: what structures do these give rise to, what are symmetries of these structures and can we systematically describe these?
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 Poincare algebra is extended to a free Lie algebra, with generalised boosts and translations that no longer commute
Summary
The Poincare∞ algebra represents an infinite generalisation of the Lorentz and translation generators. The corresponding coset space will be denoted by M∞ and is associated with the remaining generalised translation generators Pa(m) for all m ≥ 0 and a representative can be written locally as g = exp xa(m)Pa(m) , m=0. The non-linear transformations of the individual coordinates under the generalised translations follow in the standard way from the coset construction. We do this by considering left multiplication by g0 and computing the effect infinitesimal transformation induced on the coordinates via g0gh−1 = exp.
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