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Alexander N. Jourjine

Publications and source records attributed to Alexander N. Jourjine.

8 recordsLinked to original sources
arXiv2012

Unified Lepto-Quark Mixing

We describe a solution to a long standing puzzle about the difference in textures of quark CKM and lepton PMNS mixing matrices by deriving their common representation. We show how the difference in texture of the two matrices arises from assignment of lepton and quark pairs to different representation of a discrete two element symmetry group. The symmetry is absent in the Standard Model. It appears if, instead of Dirac spinors, one describes fermions in terms of bi-spinors and induces essentially unique textures: tri-bimaximal for lepton and O(λ) of Wolfenstein parameterization for quark mixing.

hep-ph↗
arXiv2011

Mass Eigenstate Mixing in the 4-Generation Dirac-Kaehler Extension of the SM

We derive the canonical form of mixing of the mass eigenstates in the lepto-quark sector of the 4-generation Dirac-Kaehler extension of the SM (DK-SM) [1,2]. The 4 x 4 CKM matrix of DK-SM is expressed in terms two U(2) matrices. It depends on 2 real parameters and 3 phases. The resulting observed 3 x 3 CKM matrix exhibits previously unknown tree-level algebraic relations among its elements. The simplest two, V_ts = V_cb and V_cs = V_tb, are supported by the experimental data [3]. The 4 x 4 CKM matrix can be fully reconstructed from the experimental values of the 3 x 3 CKM matrix. Thus, except for masses of the fourth generation, the quark sector of the DK-SM theory can be reconstructed in its entirety using the 3 x 3 CKM matrix precision measurements.

hep-ph↗
arXiv2010

The Spectrum of the 4-Generation Dirac-Kaehler Extension of the SM

We compute the mass spectrum of the fermionic sector of the Dirac-Kaehler extension of the SM (DK-SM) by showing that there exists a Bogoliubov transformation that transforms the DK-SM into a flavor U(4) extension of the SM (SM-4) with a particular choice of masses and mixing textures. Mass relations of the model allow determination of masses of the 4th generation. Tree level prediction for the mass of the 4th charged lepton is 370 GeV. The model selects the normal hierarchy for neutrino masses and reproduces naturally the near tri-bimaximal and quark mixing textures. The electron neutrino and the 4th neutrino masses are related via a see-saw-like mechanism.

hep-ph↗
arXiv2010

Mass Mixing, the Fourth Generation, and the Kinematic Higgs Mechanism

We describe how to construct chiral fermion mass terms using Dirac-Kahler (DK) spinors. Classical massive DK spinors are shown to be equivalent to four generations of Dirac spinors with equal mass coupled to a background U(2,2) gauge field. Quantization breaks U(2,2) to U(2)xU(2), lifts mass spectrum degeneracy, and generates a non-trivial mass mixing matrix.

hep-ph↗
arXiv2010

Matter on granular space-time

We develop further the formalism of the non-Abelian gauge field theory on a cell complex space-time and show how the gauge-invariant action and the equations of motion for gauge fields interacting with spinors can be written without a reference to the geometrical nature of the cells of the cell complex. The general results are illustrated with examples of solutions of equations of motion for U(N) and SU(N) gauge groups.

hep-lat↗
arXiv2001

Modeling Nonlinear Dynamical Systems with Delay-differential Equations

We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial condition of a linear delay-differential system. It is further shown that the initial condition can be extended to a periodic solution of the delay-differential system if an appropriate choice of its parameters is made. As a result, any finite set of trajectories of a nonlinear dynamical system can be modeled with arbitrarily small error via a set of periodic solutions of a linear delay-differential equation. These results can be extended to some non-linear delay differential systems. One application of the method is for modeling memory and perception.

nlin.AO↗