Geno-Bragg's law and 10*xl0 representation of SU(3) symmetry for quasicrystal structures

摘要

The synthesis of quasicrystals and observation of their unexpected 10-fold symmetric diffraction pattern by D. Shechtman and co-workers 1982-1984 provide a natural bridge for bringing solid state (condensed matter) physics within the purview of Santilli's 1967-2006 Lie-admissible generalization of quantum mechanics (QM) under the name "hadronic" mechanics (HM) via our recent non-unitary scattering theory of HM for deep-inelastic e‐ — p and e+ — e‐ scattering processes. This is achieved in this paper by a re-formulation and elaboration of Bragg's law of diffraction for quasicrystals under the title Geno-Bragg's law which permits identification of the deformed quasicrystalline state with 10*xl0 representation of SU(3) symmetry. Essentially, because only l-,2-,3-,4- and 6-fold but not 5-fold point symmetry of perfectly periodic crystal lattice are allowed in 3-dimensional (3D) real or reciprocal lattice space, a (non-unitary) deformation of the allowed (cubic) 4-fold and (hexagonal) 6-fold symmetry axes into a common diffraction (square-hexagon) geno-plane having 10-fold point symmetry is achievable as envisaged in HM. As a result, the current icosahedron approximant structure is replaced by cube-hexagon genospace structure that permits determination of atomic distribution in quasicrystals as holographic (periodic) structure. Further elaboration of Geno-Bragg's law to high energy (relativistic) deep-inelastic scattering processes described by current-current interaction models of neutron synthesis/decay is applied to the determination of the structure of the neutron and the implications for geno-renormalization of mass and the ratios of the masses of the elementary particles are discussed.