Zero mass as a Borel structure

2025/06/07 by Saar, Rein, Groote, Stefan
#FOS: Physical sciences #General Physics (physics.gen-ph)

paper · doi:10.48550/arxiv.2506.12079

Abstract

The Lorentz group Lor_1,3=SO₀(1,3) has two point fixgroups, namely SO(3) for time-like translations and SO₀(1,1)× R² 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.

Citations

• Complex hidden symmetries in real spacetime and their algebraic structures
• Poincare field theory for massive particles
• Poincare field theory for massless particles
• Algebraic Quantum Field Theory and Causal Symmetric Spaces
• Bundle Structure of Massless Unitary Representations of the Poincaré Group
• Spin operators and representations of the Poincaré group

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