Structure of a composite system in motion in relativistic quantum mechanics

Unlike in nonrelativistic quantum mechanics, the structure of a relativistic system of bound particles is intrinsically coupled with the overall translational motion of the system. This is illustrated by means of a solvable two-body model in one space dimension. The model is described in terms of the two-body Dirac equation with an interaction in the form of the δ function. Although the equation is not manifestly covariant, relativistic covariance of the model is confirmed by constructing the Lorentz-boost operator. When boosted the system exhibits exact Lorentz contraction. It is pointed out that the ‘‘form factor’’ of the bound state, which simulates the form factor of the deuteron determined by electron scattering, is not as simply related to the density distribution in the system as is often taken for granted.