Nonlinear Dirac soliton in an external field

The behaviour of the nonlinear Dirac soliton in an external potential in 1+1 dimensions is examined by means of a collective variable ansatz and also by solving the nonlinear Dirac equation numerically. When the potential is linear with respect to coordinate x, the motion of the soliton centroid is found to be consistent with the classical relativistic equation of motion for a point particle. For a general potential there is a deviation from the behaviour of the corresponding classical point particle. This deviation can be interpreted as being caused by the finite size of the soliton.