Isotopic liftings of Clifford algebras and applications in elementary particle mass matrices

Isotopic liftings of algebraic structures are investigated in the context of Clifford algebras, where it is defined a new product involving an arbitrary, but fixed, element of the Clifford algebra. This element acts as the unit with respect to the introduced product, and is called isounit. We construct isotopies in both associative and non-associative arbitrary algebras, and examples of these constructions are exhibited using Clifford algebras, which although associative, can generate the octonionic, non-associative, algebra. The whole formalism is developed in a Clifford algebraic arena, giving also the necessary pre-requisites to introduce isotopies of the exterior algebra. The flavor hadronic symmetry of the six u,d,s,c,b,t quarks is shown to be exact, when the generators of the isotopic Lie algebra su(6) are constructed, and the unit of the isotopic Clifford algebra is shown to be a function of the six quark masses. The limits constraining the parameters, that are entries of the representation of the isounit in the isotopic group SU(6), are based on the most recent limits imposed on quark masses.Comment: 19 page

SCREENING OF THE SHORT-RANGE POTENTIAL BY THE LOCAL FIELD CORRECTION IN THE LATTICE DYNAMICS OF VANADIUM

The dielectric formulation of the local field correction to the dynamical matrix for phonon dispersion relation in d-band metals in the transition-metal model potential approximation is re-examined, with a view to explore its influence on the shortrange (Born-Mayer) interatomic force contribution to the dynamical matrix. It is observed that the off-diagonal components of the inverse dielectric matrix, which determine the local field correction, make contributions that tend to cancel or "screen" the Born-Mayer contribution, just as the diagonal components of the inverse dielectric matrix tend to provide screening of the long range (Coulombic) contribution. Numerical calculation for vanadium shows that the cancellation of the Born-Mayer contribution to the dynamical matrix by the local field correction is physically significant, and leads to a better understanding of the soft modes in the phonon spectra of body-centered cubic transition metals

Modeling of the atomic ordering processes in Fe3Al intermetallics by the monte carlo simulation method combined with electronic theory of alloys

The evolution of atomic ordering processes in Fe3Al has been modeled by the Monte Carlo (MC) simulation method combined with the electronic theory of alloys in pseudopotential approximation. The magnitude of atomic ordering energies of atomic pairs in the Fe3Al system has been calculated by means of electronic theory in pseudopotential approximation up to sixth coordination spheres and subsequently used as input data for MC simulation for more detailed analysis for the first time. The Bragg–Williams long-range order (LRO) and Cowley–Warren short-range order (SRO) parameters have been calculated from the equilibrium configurations attained at the end of MC simulation for each predefined temperature and Al concentration levels, which reveal the evolution of the system from DO3 → B2 → disordered state as temperature increases. The variation of ordering parameters with temperature has identified the transition temperature from DO3 → B2 type superlattice, and from B2 → disordered (a) solid solution at about 540 °C and .900 °C, respectively, showing good qualitative agreement with experimental results. The results of the present study imply that combination of electronic theory of alloys in pseudopotential approximation with MC simulation can be successfully applied for qualitative or semiquantitative analysis of energetical and structural characteristics of atomic ordering processes in Fe3Al intermetallics