Abstract
In this Letter we study an infinite extension of the Galilei symmetry group in any dimension that can be thought of as a nonrelativistic or post-Galilean expansion of the Poincaré symmetry. We find an infinite-dimensional vector space on which this generalized Galilei group acts and usual Minkowski space can be modeled by our construction. We also construct particle and string actions that are invariant under these transformations.
Highlights
In this Letter we study an infinite extension of the Galilei symmetry group in any dimension that can be thought of as a nonrelativistic or post-Galilean expansion of the Poincaresymmetry
In this Letter, we exhibit a universal scheme for obtaining post-Galilean expansions of nonrelativistic systems by means of their symmetry algebras, starting from the Galilei algebra G
In order to understand the action of the symmetry algebra (2) on these coordinates we focus on the boosts
Summary
In this Letter we study an infinite extension of the Galilei symmetry group in any dimension that can be thought of as a nonrelativistic or post-Galilean expansion of the Poincaresymmetry. The non-relativistic gravity theory of Newton is only invariant under the Galilei group and it is not known how to obtain the associated (Newton– Cartan) Lagrangian from the relativistic Einstein-Hilbert action. Corrections to the nonrelativistic Newtonian theory at higher order in 1=c are famously important for the original experimental evidence for general relativity; see, for example, Refs. The quantum-mechanical Breit equation describes corrections of order v=c to the two-body problem for electrons but it is not invariant under Lorentz transformations [19]. In this Letter, we exhibit a universal scheme for obtaining post-Galilean expansions of nonrelativistic systems by means of their symmetry algebras, starting from the Galilei algebra G.
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