Symmetries of post-Galilean expansions

TL;DR

This paper explores an infinite-dimensional extension of the Galilei symmetry group, modeling Minkowski space and constructing invariant particle and string actions, thus broadening the understanding of non-relativistic symmetries.

Contribution

It introduces an infinite extension of the Galilei group applicable in any dimension, with new invariant actions for particles and strings.

Findings

Infinite-dimensional symmetry group acting on Minkowski space

Construction of invariant particle and string actions

Extension of Galilei symmetry to post-Galilean regime

Abstract

In this letter we study an infinite extension of the Galilei symmetry group in any dimension that can be thought of as a non-relativistic or post-Galilean expansion of the Poincare 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.