Relativistic two-body equation based on the extension of the SL(2,C) group

A new approach to the two-body problem based on the extension of the SL(2,C) group to the Sp(4,C) one is developed. The wave equation with various forms of including the interaction for the system of the spin-1/2 and spin-0 particles is constructed. For this system, it was found that the wave equation with a linear confinement potential involved in the non-minimal manner has an oscillator-like form and possesses the exact solution.