  The amplitudes for boson-boson and fermion-boson interactions are calculated
in the second order of perturbation theory in the Lobachevsky space. An
essential ingredient of the used model is the Weinberg's $2(2j+1)$ component
formalism for describing a particle of spin $j$, recently developed
substantially. The boson-boson amplitude is then compared with the two-fermion
amplitude obtained long ago by Skachkov on the ground of the hamiltonian
formulation of quantum field theory on the mass hyperboloid, $p_0^2 -{\bf
p}^2=M^2$, proposed by Kadyshevsky. The parametrization of the amplitudes by
means of the momentum transfer in the Lobachevsky space leads to same spin
structures in the expressions of $T$ matrices for the fermion and the boson
cases. However, certain differences are found. Possible physical applications
are discussed.
