Zero mass as a Borel structure

TL;DR

This paper explores how the Borel structure of the Lorentz group relates to the concept of masslessness in particles, emphasizing the role of underlying Lie group symmetries over physical mass.

Contribution

It introduces the idea that massless versus massive particles can be distinguished by the Borel structure of the Lorentz group, not just physical properties.

Findings

Borel structure provides appropriate helicities for massless particles

Light-like translations relate to a line fixgroup leading to Borel structure

Mass vs. massless distinction is rooted in Lie group symmetry

Abstract

The Lorentz group Lor$_{1,3}=$SO$_0(1,3)$ has two point fixgroups, namely SO$(3)$ for time-like translations and SO$_0(1,1)\times R^2$ for light-like translations. However, for light-like translations it is reasonable to consider a line fixgroup that leads to the Borel structure of the Lorentz group and gives appropriate helicities for massless particles. Therefore, whether a particle is massless or massive is not so much a physical question but rather a question of the underlying Lie group symmetry.