Period doubling and the full structure of the periodic table (including Seaborg and 10-period extensions plus antimatter) arise as the weight diagram of so(4,4) split by its fourth Cartan generator into a double SO(4,2)-tower.
The Periodic Table and the Group SO(4,4)
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abstract
The periodic system of chemical elements is represented within the framework of the weight diagram of the Lie algebra of the fourth rank of the rotation group of an eight-dimensional pseudo-Euclidean space. The hydrogen realization of the Cartan subalgebra and Weyl generators of the group algebra is studied. The root structure of the subalgebras of the group algebra of a conformal group in the framework of a twofold covering is analyzed. Based on the analysis, the Cartan-Weyl basis of the group algebra is determined. The root and weight diagrams are constructed. A mass formula associated with each node of the weight diagram is introduced. Spin is interpreted as the fourth generator of the Cartan subalgebra, whose two eigenvalues correspond to two three-dimensional projections of the weight diagram containing elements of the periodic system from hydrogen to moscovium (the first projection) and from helium to oganesson (the second projection). One of the main advantages of the proposed group-theoretic construction of the periodic system is the natural inclusion of antimatter in the general scheme.
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The Periodic Table and the Group SO(4,4): II. Double SO(4,2)-tower
Period doubling and the full structure of the periodic table (including Seaborg and 10-period extensions plus antimatter) arise as the weight diagram of so(4,4) split by its fourth Cartan generator into a double SO(4,2)-tower.