Linear equations of motion for massless particles of any spin in any even dimensional spaces

TL;DR

This paper proves that Poincare symmetry uniquely determines linear equations of motion for massless particles of any spin in even-dimensional spaces, focusing on spin degrees of freedom without gauge symmetry.

Contribution

It establishes that in even dimensions, Poincare symmetry constrains massless particle equations to be linear in momentum, for any spin and without gauge considerations.

Findings

Equations are linear in momentum for massless particles in even dimensions.

The proof applies to fields with no gauge symmetry.

Examples illustrate the general result.

Abstract

It is proven that the Poincare symmetry determines equations of motion, which are for massless particles of any spin in d-dimensional spaces linear in the momentum. The proof is made only for even d and for fields with no gauge symmetry. We comment on a few examples. We pay attention only to spin degrees of freedom.