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

Kulikov, D. A.; Tutik, R. S.; Yaroshenko, A. P.

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

Authors

Kulikov, D. A.

Tutik, R. S.

Yaroshenko, A. P.

Description

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.
9 pages, no figures