The Periodic Table and the Group SO(4,4)

TL;DR

This paper models the periodic table using the Lie algebra of the SO(4,4) group, revealing a group-theoretic structure that includes antimatter and interprets spin as a generator within this framework.

Contribution

It introduces a novel group-theoretic approach to the periodic system based on the SO(4,4) Lie algebra, connecting chemical elements with advanced mathematical structures.

Findings

Root and weight diagrams of the group algebra are constructed.

A mass formula linked to the weight diagram nodes is proposed.

Spin is interpreted as a generator with eigenvalues corresponding to element projections.

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.