UDC 539.12 Description of Lepton and Baryon Phases in Skyrme–Faddeev Spinor Model V. I. Molotkov Department of Theoretical Physics and Mechanics Peoples’ Friendship University of Russia 6, Miklukho-Maklaya str., Moscow, Russia, 117198 8-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. <...> Key words and phrases: 8-spinor, topological charge, solitons, homotopy groups, Brioshi identity, Skyrme–Faddeev model, Hopf index. 1. <...> Nonlinear 8-spinor field theory the Mie electrodynamics within the scope of effective 8-spinor field model with the Lagrangian including Higgs-like potential and higher degrees of the invariant AµAµ. <...> For the classification of all possible chiral type models, the special 8-spinor Brioschi identity is used [2]: jµjµ −˜ jµ = s2 +p2 +v2 +a2. jµ˜ In this identity the following quadratic spinor quantities are introduced: S = ψψ, p = iψγ5ψ, v = ψλψ, a = iψγ5λψ, jµ = ψγµψ, ˜ (1) jµ = ψγµγ5ψ, with ψ = ψ+γ0 and matrix λ = σi⊗I4 standing for the Pauli matrices in the isotopic spinor space. <...> It serves as the generator of the third homotopy group π3(S3) = Z. The similar idea to describe leptons as topological solitons <...>