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A new technique for constructing the relativistic wave equation for thetwo-body system composed of the spin-1/2 and spin-0 particles is proposed. Themethod is based on the extension of the SL(2,C) group to the Sp(4,C) one. Theobtained equation includes the interaction potentials, having both theLorentz-vector and Lorentz-tensor structure, exactly describes the relativistickinematics and possesses the correct one-particle limits. The comparison withresults of other approaches to this problem is discussed.

A new approach to the relativistic treatment of the fermion-boson system, based on the extension of the SL(2,C) group