Born's group and Generalized isometries

TL;DR

This paper introduces the Born group, a new class of spacetime transformations in Minkowski space, and explores the concept of Generalized isometries, bridging isometry groups and diffeomorphism groups.

Contribution

It defines the Born group in terms of Fermi coordinates, constructs its finite and infinitesimal transformations, and introduces the concept of Generalized isometry groups.

Findings

Defined the Born group as a set of spacetime transformations.

Constructed explicit infinitesimal transformations of the Born group.

Introduced the concept of Generalized isometry groups, connecting known symmetry groups.

Abstract

We define the Born group as the group of transformations that leave invariant the line element of Minkowski's spacetime written in terms of Fermi coordinates of a Born congruence. This group depends on three arbitrary functions of a single argument. We construct implicitly the finite transformations of this group and explicitly the corresponding infinitesimal ones. Our analysis of this group brings out the new concept of Generalized group of isometries. The limitting cases of such groups being, at one end, the Groups of isometries of a spacetime metric and, at the other end, the Group of diffeomorphisms of any spacetime manifold. We mention two examples of potentially interesting generalizations of the Born congruences.