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 . 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).
 Nduka, A. (2012) The Geometrical Theory of Science. Applied Mathematics, 3, 1598-1600.
 Nduka, A. (2013) The Neutrino Mass. Applied Mathematics, 4, 310-313.