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New classification of particles is proposed. This classification is based on U(Nf,g) ×SU(3c)×SU(4, fs)×O(3) -group, where U(Nf,g) corresponds to the particle generations, SU(3,c) - to the color, SU(4,fs) - to the flavor and the spin (instead of known SU(6,fs) -group), and O(3) - to the orbital excitation with the L -momentum. The Nf -number equals the quantity of fermion generations. From the convergence of the integrals corresponding to the Green functions for generalized Dirac equations and the continuity of these functions it follows that the minimal quantity of the Nf -number equals six. The homogeneous solutions of derived equations are sums of fields, corresponding to particles with the same values of the spin, the electric charge, the parities, but with different masses. Such particles are grouped into the kinds (families, dynasties) with members which are the particle generations. For example, the electronic kind (e1 = e, e2 = μ, e3 =τ , e4, e5, e6, ), the kind of up-quarks (U1 = u, U2 = c, U3 = t, U4, U5, U6, ⋅⋅ ), and the kind of down-quarks (D1 = d, D2 = s, D4 = b, D4, D5, D6, ⋅⋅ ) can exist. Massless neutrino can be one only. The photonic and the gluonic kinds must include massive particles in addition to usual the photon and the gluon. At NF = 6 the nucleons and Δ(1232) belong to the 56×1×20×1 - representation. Lagrangians for the generalized Dirac equations of arbitrary order are derived.

Classification of Particles at Arbitrary Quantity of Generations. I. Hadrons