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Amplitudes for fermion-fermion, boson-boson and fermion-boson interactionsare calculated in the second order of perturbation theory in the Lobachevskyspace. An essential ingredient of the model is the Weinberg's 2(2j+1)-componentformalism for describing a particle of spin j. The boson-boson amplitude isthen compared with the two-fermion amplitude obtained long ago by Skachkov onthe basis of the Hamiltonian formulation of quantum field theory on the masshyperboloid, p_0^2 - p^2=M^2, proposed by Kadyshevsky. The parametrization ofthe amplitudes by means of the momentum transfer in the Lobachevsky space leadsto same spin structures in the expressions of T-matrices for the fermion caseand the boson case. However, certain differences are found. Possible physicalapplications are discussed.

Fermion-fermion and boson-boson amplitudes: surprising similarities