Wave equation of massless particles of arbitrary helicity

TL;DR

This paper derives a general wave equation for massless particles with any helicity from fundamental principles, establishing a position operator and comparing with existing literature.

Contribution

It introduces a new derivation of the wave equation for massless particles of arbitrary helicity based on Poincaré group representations and defines a novel localization concept.

Findings

Derived the wave equation from first principles.

Defined a position operator for massless particles.

Compared results with previous literature.

Abstract

In this work, we derive from first principles the relativistic wave equation of massless particles of arbitrary helicity. We start from unitary projective irreducible representations of the restricted Poincar\'e group. We define a weaker notion of localization and find, in particular, a position operator for any massless particle of arbitrary helicity. Therefore, having the position representation for these particles, we obtain the wave equations in this representation. We compare our results with previous findings in the literature.