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The amplitudes for boson-boson and fermion-boson interactions are calculatedin the second order of perturbation theory in the Lobachevsky space. Anessential ingredient of the used model is the Weinberg's $2(2j+1)$ componentformalism for describing a particle of spin $j$, recently developedsubstantially. The boson-boson amplitude is then compared with the two-fermionamplitude obtained long ago by Skachkov on the ground of the hamiltonianformulation of quantum field theory on the mass hyperboloid, $p_0^2 -{\bfp}^2=M^2$, proposed by Kadyshevsky. The parametrization of the amplitudes bymeans of the momentum transfer in the Lobachevsky space leads to same spinstructures in the expressions of $T$ matrices for the fermion and the bosoncases. However, certain differences are found. Possible physical applicationsare discussed.Comment: REVTeX 3.0 file. 12pp. Substantially revised version of IFUNAM  preprints FT-93-24, FT-93-3

Interactions of aj=1 boson in the 2(2j+1) component theory