An extension of Poincar\'e group abiding arbitrary acceleration

TL;DR

This paper extends the Poincaré group to include arbitrary acceleration transformations using Fermi-Walker coordinates, revealing an infinite-dimensional, Abelian extension where acceleration boosts commute with each other and translations.

Contribution

It introduces an infinite-dimensional Abelian extension of the Poincaré algebra that incorporates arbitrary acceleration transformations in relativistic reference frames.

Findings

Extension is infinite dimensional and Abelian.

Acceleration boost generators commute with translations.

The extension differs from Lorentz boosts in commutation properties.

Abstract

The class of accelerated reference frames has been studied, on the basis of Fermi-Walker coordinates. The infinitesimal transformations connecting two of these frames has been obtained, and also their commutation relations. The outcome is an infinite dimensional extension of the Poincar\'e algebra. Although this extension turns out to be Abelian, and hence trivial, it is noteworthy that, contrarily to what happens with Lorentz boosts, acceleration boost generators commute with each other and with translation generators.