Massless particles in five and higher dimensions

TL;DR

This paper extends Wigner's operator equation for massless particles to five and higher dimensions, providing a new framework for understanding their properties in these extended spacetimes.

Contribution

It introduces a five-dimensional analogue of Wigner's equation and generalizes it to higher dimensions, advancing the theoretical understanding of massless particles beyond four dimensions.

Findings

Derived a five-dimensional version of Wigner's equation for massless particles.

Generalized the equation to higher dimensions beyond five.

Provides a theoretical foundation for studying massless particles in higher-dimensional theories.

Abstract

We describe a five-dimensional analogue of Wigner's operator equation ${\mathbb W}_a = \lambda P_a$, where ${\mathbb W}_a $ is the Pauli-Lubanski vector, $P_a$ the energy-momentum operator, and $\lambda$ the helicity of a massless particle. Higher dimensional generalisations are also given.