Superfield equations of motion for D = 10 type IIB Dirichlet super-9-brane are obtained from the generalized action principle.The geometric equations containing fermionic superembedding equations and constraints on the generalized field strength of Abelian gauge field are separated from the proper dynamical equations and are found to contain these dynamical equations among their consequences.The set of superfield equations thus obtained involves a Spin(1, 9) group valued superfield h β α whose leading component appears in the recently obtained simplified expression for the κ-symmetry projector of the D9-brane. The Cayley image of this superfield coincides (on the mass shell) with the field strength tensor of the world volume gauge field characteristic for the Dirichlet brane.The superfield description of the super-9-brane obtained in this manner is known to be, on the one hand, the nonlinear (Born-Infeld) generalization of supersymmetric Yang-Mills theory and, on the other hand, the theory of partial spontaneous breaking of D = 10 N = IIB supersymmetry down to D = 10 N = 1.

We construct the manifestly Lorenz-invariant formulation of the N = 1, D=4 massive superparticle with tensorial central charges. The model contains a real parameter k and at k≠0 possesses one κ-symmetry while at k=0 the number of κ-symmetry is two. The equivalence of the formulations at all k≠0 is obtained. The local transformations of κ-symmetry are written. It is considered using the index spinor for construction of the tensorial central charges. The equivalence at classical level between the massive D=4 superparticle with one κ-symmetry and the massive D=4 spinning particle is obtained.

The first and second covariant quantization of a free massless d = 4 superparticle with pure gauge auxiliary spinor variables have been carried out.

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We construct the manifestly Lorentz-invariant twistorial formulation of the N = 1 D = 4 superparticle with tensorial central charges which describes massive and massless cases in a uniform manner. The tensorial central charges are realized in terms of even spinor variables and central charge coordinates. The full analysis of the number of conserved supersymmetries has been carried out. In the massive case the superparticle preserves 1/4 or 1/2 of target-space supersymmetries whereas the massless superparticle preserves two or three supersymmetries.