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 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.

arXiv comment23 pages

References in corpus (20)

• Action Principle for Newtonian Gravity
• Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity
• Expanding Lie (super)algebras through abelian semigroups
• Standard General Relativity from Chern-Simons Gravity
• Torsional Newton-Cartan gravity from the large $c$ expansion of General Relativity
• Wess-Zumino term for the AdS superstring and generalized Inonu-Wigner contraction
• Gravity between Newton and Einstein
• Post-Newtonian extension of the Newton-Cartan theory
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Lie Algebra Expansions and Actions for Non-Relativistic Gravity
• Standard and Generalized Newtonian Gravities as ``Gauge'' Theories of the Extended Galilei Group - I: The Standard Theory
• Infinite Sequence of Poincare Group Extensions: Structure and Dynamics
• On free Lie algebras and particles in electro-magnetic fields
• Generalized Poincare algebras and Lovelock-Cartan gravity theory
• Three-Dimensional Extended Newtonian (Super)Gravity
• Oddity in nonrelativistic, strong gravity
• Galilean free Lie algebras
• (In)finite extensions of algebras from their Inonu-Wigner contractions
• Symmetries of post-Galilean expansions
• Infinite S-Expansion with Ideal Subtraction and Some Applications

Cited by in corpus (2)

• Colourful Poincaré symmetry, gravity and particle actions
• BMS algebras in 4 and 3 dimensions, their quantum deformations and duals