Conformal Generators and Doubly Special Relativity Theories

TL;DR

This paper explores the connection between doubly special relativity theories and conformal group generators, proposing a new generator to deform the conformal group and analyze light cone modifications.

Contribution

It introduces a new generator derived from dimensional reduction to relate DSR modifications to conformal group structures.

Findings

Modified Lorentz boosts relate to conformal group generators.

A new generator can deform the conformal group to match DSR theories.

Light cone structures can remain unchanged in higher-dimensional space.

Abstract

In this paper, the relation between the modified Lorenz boosts, proposed in the doubly relativity theories and a linear combination of Conformal Group generators in $R^{1,d-1}$ is investigated. The introduction of a new generator is proposed in order to deform the Conformal Group to achieve the connection conjectured. The new generator is obtained trough a formal dimensional reduction from a free massless particle living in a $R^{2,d}$ space. Due this treatment it is possible to say that even DSR theories modify light cone structure in $R^{1,d-1}$, it could remains, in some cases, untouched in $R^{2,d}$.