A Projective Interpretation of Some Doubly Special Relativity Theories

TL;DR

This paper explores a geometric framework using projective actions of the orthogonal group to interpret Doubly Special Relativity theories, revealing their connection to known transformations and enabling the development of new transformation types.

Contribution

It provides a novel geometric interpretation of Doubly Special Relativity transformations through projective actions, linking them to the orthogonal group and introducing new transformation possibilities.

Findings

Doubly Special Relativity transformations are shown to be projective actions of the orthogonal group.

The formalism connects known transformations like Fock--Lorentz and Magueijo--Smolin to a unified geometric framework.

New types of transformations are derived from the projective formalism.

Abstract

A class of projective actions of the orthogonal group on the projective space is being studied. It is shown that the Fock--Lorentz, and Magueijo--Smolin transformations known as Doubly Special Relativity are such transformations. The formalism easily lead to new type transformations.