Group Theoretical Description of the Periodic System

Abstract

The group theoretical description of the periodic system of elements in the framework of the Rumer–Fet model is considered. We introduce the concept of a single quantum system, the generating core of which is an abstract C*-algebra. It is shown that various concrete implementations of the operator algebra depend on the structure of the generators of the fundamental symmetry group attached to the energy operator. In the case of the generators of the complex shell of a group algebra of a conformal group, the spectrum of states of a single quantum system is given in the framework of the basic representation of the Rumer–Fet group, which leads to a group-theoretic interpretation of the Mendeleev’s periodic system of elements. A mass formula is introduced that allows giving the termwise mass splitting for the main multiplet of the Rumer–Fet group. The masses of elements of the Seaborg table (eight-periodic extension of the Mendeleev table) are calculated starting from the atomic number Z=3 and going to Z=220. The continuation of the Seaborg homology between lanthanides and actinides is established with the group of superactinides. A 10-periodic extension of the periodic table is introduced in the framework of the group-theoretic approach. The multiplet structure of the extended table’s periods is considered in detail. It is shown that the period lengths of the system of elements are determined by the structure of the basic representation of the Rumer–Fet group. The theoretical masses of the elements of 10th and 11th periods are calculated starting from Z=221 and going to to Z=364. The concept of hypertwistor is introduced.

How the Modified Bertrand Theorem Explains Regularities and Anomalies of the Periodic Table of Elements

“…read chapter 5 of (Scerri and Restrepo, 2018) insisted that, if properly interpreted, the Madelung rule is applicable for the whole periodic system of elements. This fact is supported by the group-theoretic considerations leading to the conclusion that the underlying symmetry of the periodic table is SO(4,2) and, using this symmetry, that the Madelung rule(without exceptions) follows from the group theoretic considerations (Fet, 2016), (Thussen and Ceulemans, 2017), (Varlamov, 2018) As we just mentioned, theory of quantum defects should, in principle, provide needed answer. But mentioned results based on relativistic calculations known from the theory of theory of perihelion shift are not the only ones which can be used as point of departure.…”

“…It is exact analog of the periodic system of chemical elements 20 . Not surprisingly, methods of particle physics had been recently applied back to periodic system of elements (Fet, 2016), (Varlamov, 2018).…”

“…Initially, the (quark model, quark symmetry) ideas of particle physics were used for classification of elements in the periodic system of elements by Fet (Fet, 2016). These were also discussed in some detail in (Thussen and Ceulemans, 2017) and by (Varlamov, 2018) without emphasis on the Madelung rule though. The task of this and future publications is to demonstrate that the noticed fruitful cross-fertilization between just mentioned results of physics and chemistry might potentially yield new and significant results both in physics and chemistry if the exceptions to the Madelung rule in the atomic physics are to be studied.…”

On Mass Quantization

“…При конкретном выборе группы 𝐺 собственные векторы оператора энергии 𝐻 с дискретными собственными значениями задают стационарные состояния системы 𝐔. Так, при 𝐺 SO 1,3 (группа Лоренца) спектр материи есть спектр «элементарных частиц» [53; 54], полный список которых представлен в Particle Data Group [55]. При 𝐺 SO 2,4 , где SO 2,4 -конформная группа, приходим к периодической системе химических элементов [56][57][58][59][60]. В этом случае стационарные состояния системы 𝐔 соответствуют атомам элементов.…”