The freeon unitary group procedure and the structure of matter

Abstract

There is presented a novel, coherent procedure, based on the unitary group, for the computation of the spectra of atoms, molecules, solids, nuclei, and elementary particles. These spectra cover a truly remarkable energy range from a fraction to billions of electron volts. The procedure employs freeon orbitals that are free of energetically inert orbitals; e.g., ordinary spin orbitals for electrons, isospin orbitals for nuclei, and the product of ordinary spin orbitals and color orbitals for baryons. The Pauli principle requires the freeon spaces to be conjugate to the inert spaces. The spaces are spanned by Gel'fand states that have a simple, compact, pictorial representation in the form of Gel'fand structures (tableaux). The Hamiltonian for all systems is a second degree polynomial in the generators of the unitary group with parameters that determine the spectral scale and distribution and whose matrix elements are computed Lie algebraically. The unitary group supplies the unitary group quantum number and is the head group of chains of groups that supply additional quantum numbers.