Mass, zero mass and ... nophysics

TL;DR

This paper argues that massless particles are fundamentally different from massive ones, proposing a new symmetry framework based on solvable groups instead of traditional semisimple groups, impacting particle helicity understanding.

Contribution

It introduces a novel approach replacing semisimple symmetry groups with solvable groups for massless particles, extending Wigner's little group to include additional generators.

Findings

Massless particles cannot be viewed as limits of massive particles.

The symmetry group for massless particles is a maximal solvable subgroup, ${ m Bor}_{1,3}$.

Helicity properties are linked to the structure of the extended symmetry group.

Abstract

In this paper we demonstrate that massless particles cannot be considered as limiting case of massive particles. Instead, the usual symmetry structure based on semisimple groups like $U(1)$, $SU(2)$ and $SU(3)$ has to be replaced by less usual solvable groups like the minimal nonabelian group ${\rm sol}_2$. Starting from the proper orthochronous Lorentz group ${\rm Lor}_{1,3}$ we extend Wigner's little group by an additional generator, obtaining the maximal solvable or Borel subgroup ${\rm Bor}_{1,3}$ which is equivalent to the Kronecker sum of two copies of ${\rm sol}_2$, telling something about the helicity of particle and antiparticle states.