TITLE:
The Geometrical Theory of the Structure of Nuclei, Atoms, and Molecules
AUTHORS:
Amagh Nduka
KEYWORDS:
Reducibility, Irreducibility, Periodicity, Fermion, Quantum Number, Index
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.15,
August
5,
2014
ABSTRACT: Quantum
geometrodynamics (QGD) has established the following fundamental facts: First, every
elementary particle is the physical realization of a certain irreducible
4-quantum operator of spin (rank) 0, 1/2 or 1.
A photon (boson) is the physical realization of an irreducible 4-quantum operator
of spin zero. A fermion is the physical realization of an irreducible 4-quantum
operator of spin 1/2. A graviton (boson) is the physical realization
of an irreducible 3-quantum operator of spin zero, and the Ws and mesons
(bosons) are the physical realizations of irreducible 3-quantum operator of
rank one. Second, the particles of every composite fermion system (nuclei,
atoms, and molecules) reside in a certain 4-quantum space which is partitioned
into an infinite set of subspaces of dimension 4n (n = 1, 2, 3, L,∞; n is the index of the subspace and n is
called principal quantum number by physicists, and period by chemists) each of
which is reducible to a set of 2-level cells [1]. With these two fundamental facts, the
complexities associated with atomic, nuclear, and molecular many-body problems
have evaporated. As an application of the reducibility scenario we discuss in
this paper the explicit construction of the periodic table of the chemical
elements. In particular we show that each chemical element is characterized by
a state ket ｜En;
l, m1; s, ms〉where l is
orbital angular momentum, s = 1/2, En
= E1 + khv (k = 1, 2, 3, L, ∞, E1 is the
Schr?dinger first energy level, and v is the
Lamb-Retherford frequency).