A remark about unitary representations of Lorentz group and an equation for zero mass particles

TL;DR

This paper explores the expansion of wave functions of massless particles with fixed helicity over unitary irreducible Lorentz group representations, deriving an equation in the relativistic configuration space as an analog to Fourier transformation.

Contribution

It introduces a novel method for deriving equations for massless particles using Lorentz group representations and their expansion of wave functions.

Findings

Derived an equation for zero mass particles in relativistic configuration space.

Established a Fourier-like transformation based on Lorentz group representations.

Provided insights into the structure of wave functions for massless particles.

Abstract

In the present note the expansion of the wave function of a massless particle (with the definite value of its helicity) over the untary irreducible representaions of the Lorentz group (defined on the light cone) is used as for the analog of the Fourier transformation for deriving of an equation in the relativistic configuration representation.