The relativistic three-body problem is approached via the extension of the SL(2,C) group to the Sp(4,C) one. In terms of Sp(4,C) spinors, a Dirac-like equation with three-body kinematics is composed. After introducing the linear in coordinates intera
ction, it describes the spin-1/2 oscillator. For this system, the exact energy spectrum is derived and then applied to fit the Regge trajectories of baryon N-resonances in the (E^2,J) plane. The model predicts linear trajectories at high total energy E with some form of nonlinearity at low E.
