The periodic table is embedded in a weight diagram of so(4,4) with the fourth Cartan generator assigned to spin, yielding two three-dimensional projections for the two spin values.
Lorentz group and mass spectrum of elementary particles
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Mass spectrum of localized states (elementary particles) of single quantum system is studied in the framework of Heisenberg's scheme. Localized states are understood as cyclic representations of a group of fundamental symmetry (Lorentz group) within a Gelfand-Neumark-Segal construction. It is shown that state masses of lepton (except the neutrino) and hadron sectors of matter spectrum are proportional to the rest mass of electron with an accuracy of $0,41\%$.
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The Periodic Table and the Group SO(4,4)
The periodic table is embedded in a weight diagram of so(4,4) with the fourth Cartan generator assigned to spin, yielding two three-dimensional projections for the two spin values.