  We establish soliton-like asymptotics for finite energy solutions to the
Dirac equation coupled to a relativistic particle. Any solution with initial
state close to the solitary manifold, converges in long time limit to a sum of
traveling wave and outgoing free wave. The convergence holds in global energy
norm. The proof uses spectral theory and the symplectic projection onto
solitary manifold in the Hilbert phase space.
