论文标题
自由的谎言代数方法，用于弯曲校正到平坦的时空
A free Lie algebra approach to curvature corrections to flat space-time
论文作者
论文摘要
我们研究了一种系统的方法，以在曲率尺度上逐步订购平面时订单的等轴测代数曲率校正。庞加莱代数扩展到一个自由的谎言代数，并具有不再通勤的广义提升和翻译。附加发电机满足级别排序并在该顺序编码曲率校正。这最终导致了一个无限维代数，我们称之为poincaré$ {} _ \ infty $，我们表明它包含一个（a）ds商。我们讨论了该无限维代数的非线性实现，并基于它构建了粒子作用。后者产生一个测量方程，其中包括（a）每个顺序的ds曲率校正。
We investigate a systematic approach to include curvature corrections to the isometry algebra of flat space-time order-by-order in the curvature scale. The Poincaré algebra is extended to a free Lie algebra, with generalised boosts and translations that no longer commute. The additional generators satisfy a level-ordering and encode the curvature corrections at that order. This eventually results in an infinite-dimensional algebra that we refer to as Poincaré${}_\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.
