Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8276Research ArticleDescription of Lepton and Baryon Phases in Skyrme-Faddeev Spinor ModelMolotkovV IDepartment of Theoretical Physics and Mechanicsmolotvi@gmail.comPeoples’ Friendship University of Russia150220152737708092016Copyright © 2015,20158-spinor ﬁeld is suggested to unify Skyrme and Faddeev models describing baryons and leptons as topological solitons. In the Skyrme model the particles-solitons possess the topological charge of the degree type, which is interpreted as the baryon number. In the Faddeev model the particles are endowed with the topological invariant of the Hopf type, which is interpreted as the Lepton number. The special 8-spinor Brioschi identity is used to include leptons and baryons as two possible phases of the effective spinor ﬁeld model with Higgs potential depending on the jμjμ being added to the Lagrangian. In the present paper the generalization of the Mie electrodynamics within the scope of the eﬀective 8-spinor ﬁeld model is suggested. For this ﬁeld model the quadratic spinor quantities entering the Brioschi identity are constructed. Also we ﬁnd the symmetry groups, which generate S2- and S3-submanifolds in general S8 biquadratic spinor manifold. As a result we have the homotopy groups π3(S2) and π3(S3), which describes lepton and baryon phases. To unifying these phases, we ﬁnd common vacuum state which conserves only one component in two cases. Finally, we obtain the resulting 8-spinor model permitting uniﬁed description of baryon and lepton.8-spinortopological chargesolitonshomotopy groupsBrioshi identitySkyrme-Faddeev modelHopf index8-спинортопологический зарядсолитоныгомотопические группытождество Бриоскимодель Скирма-Фаддееваиндекс Хопфа