Very special relativity as particle in a gauge field and two-time physics

TL;DR

This paper explores the dynamics of particles in very special relativity, revealing dimensional reduction to (2+1)D, and introduces a new symmetry and a generalized action incorporating two-time physics.

Contribution

It demonstrates that particles in very special relativity effectively operate in lower dimensions and introduces a new symmetry and a generalized Lorentz-invariant action.

Findings

Massless particles travel in (2+1)D space-time.

The action can be expressed as a particle in a gauge field causing dimensional reduction.

A new symmetry for the system is identified.

Abstract

The action for a $(3+1)$-dimensional particle in very special relativity is studied. It is proved that massless particles only travel in effective $(2+1)$-dimensional space-time. It is remarkable that this action can be written as an action for a relativistic particle in a background gauge field and it is shown that this field causes the dimensional reduction. A new symmetry for this system is found. Furthermore, a general action with restored Lorentz symmetry is proposed for this system. It is shown that this new action contains very special relativity and two-time physics.