Topological Soliton Configurations in 8-Spinor Nonlinear Model

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Abstract


We study the structure of the charged topological solitons in the lepton sector of the nonlinear 8-spinor model, at small distances the closed-string approximation being used. The mass, the spin and the magnetic moment of the soliton configuration with the unit leptonic number are estimated. The model is based on the well-known 8-spinor identity suggested by the Italian geometer Brioschi. Due to the identity the Dirac current appears to be time-like 4-vector that permits one to introduce the special form of the Higgs potential depending on the current squared. Within the framework of this model the natural classification of leptons and baryons can be realized via the Higgs mechanism. Concentrating on the lepton sector we study the simplest soliton configuration endowed with the unit Hopf index playing the role of the lepton number. Investigating the behavior of solutions at large and small distances we obtain the numerical estimate of physical characteristics of the topological soliton. The special symmetry group is used in our calculation, the combined rotations in ordinary and isotopic spaces being considered. The corresponding equivariant spinor fields involve phase functions linear with respect to azimuthal and toroidal angles. This property permits one to find explicit value of the topological invariant for the axially-symmetric configuration and to investigate the dependence of the physical characteristics on topology.

Yu P Rybakov

Peoples’ Friendship University of Russia

Email: soliton4@mail.ru
Department of Theoretical Physics

N Abi Farraj

Peoples’ Friendship University of Russia

Department of Theoretical Physics

Yu Umniyati

Peoples’ Friendship University of Russia

Department of Theoretical Physics

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Copyright (c) 2013 Рыбаков Ю.П., Фарраж Н.А., Умнияти Ю.

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