Mass, zero mass and ... nophysics

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 ${\mathrm{sol}}_2$. Starting from the proper orthochronous Lorentz group ${\mathrm{Lor}}_{1,3}$ we extend Wigner's little group by an additional generator, obtaining the maximal solvable or Borel subgroup ${\mathrm{Bor}}_{1,3}$ which is equivalent to the Kronecker sum of two copies of ${\mathrm{sol}}_2$, telling something about the helicity of particle and antiparticle states.

44 pages, no figures, published version

References in corpus (4)

• Symmetry properties of conservation laws
• Conservation laws of coupled semilinear wave equations
• Weyl, Majorana and Dirac fields from a unified perspective
• Currents for Arbitrary Helicity

Cited by in corpus (3)

• Gauge dependence of the gauge boson projector
• A solvable algebra for massless fermions
• Zero mass as a Borel structure