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Mass, Zero Mass and ...Nophysics

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Abstract

In this paper we demonstrate that massless particles cannot be considered as the 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 \(\mathop {\mathrm{sol}}\nolimits _2\). Starting from the proper orthochronous Lorentz group \(\mathop {\mathrm{Lor}}\nolimits _{1,3}\) we extend Wigner’s little group by an additional generator, obtaining the maximal solvable or Borel subgroup \(\mathop {\mathrm{Bor}}\nolimits _{1,3}\) which is equivalent to the Kronecker sum of two copies of \(\mathop {\mathrm{sol}}\nolimits _2\), telling something about the helicity of particle and antiparticle states.

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Authors and Affiliations

  1. Loodus- ja Täppisteaduste valdkond, Füüsika Instituut, Tartu Ülikool, W. Ostwaldi 1, 50411, Tartu, Estonia

    R. Saar & S. Groote

  2. PRISMA Cluster of Excellence, Institut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, 55099, Mainz, Germany

    S. Groote

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  1. R. Saar
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  2. S. Groote
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Correspondence to S. Groote.

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Communicated by Zbigniew Oziewicz

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Saar, R., Groote, S. Mass, Zero Mass and ...Nophysics. Adv. Appl. Clifford Algebras 27, 2739–2768 (2017). https://doi.org/10.1007/s00006-017-0758-2

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