A Realization of the Cohen-Glashow Very Special Relativity

TL;DR

This paper demonstrates that Cohen-Glashow's Very Special Relativity can be realized within noncommutative Moyal space-time, preserving certain subgroups of the Poincaré symmetry through specific noncommutativity structures.

Contribution

It provides a novel realization of VSR as a symmetry of noncommutative space-time, linking VSR subgroups to particular noncommutativity parameters and structures.

Findings

VSR subgroups can be realized in noncommutative space-time.

Light-like noncommutativity parameter is essential for VSR realization.

Different VSR subgroups correspond to different types of noncommutativity.

Abstract

We show that the Cohen-Glashow Very Special Relativity (VSR) theory [1] can be realized as the part of the Poincar\'e symmetry preserved on a noncommutative Moyal plane with light-like noncommutativity. Moreover, we show that the three subgroups relevant to the Cohen-Glashow VSR can also be realized in the noncommutative space-time setting. For all these three cases the noncommutativity parameter $\theta^{\mu\nu}$ should be light-like ($\theta^{\mu\nu}\theta_{\mu\nu}=0$). A fixed constant noncommutativity parameter respects the T(2) subgroup of Lorentz, while for the E(2) and SIM(2) cases the form of noncommutativity among the coordinates should be of linear (Lie algebra) and quadratic (quantum group) type, respectively. We discuss some physical implications of this realization of the Cohen-Glashow VSR.