Relativistic dynamics and Lorentz contraction

Regarding the structure of a bound system of two particles in relativistic quantum mechanics we raise the following question: Does the shape of (i.e., the density distribution in) a bound system in motion always conform to Lorentz contraction? A negative possibility is illustrated by means of the Bakamjian-Thomas model which is relativistically covariant in the sense that the generators of the Poincaré algebra for the model can be constructed explicitly. The degree of deviation from Lorentz contraction will depend on the choice of the interaction. We examine another model of two interacting particles, which is based on field theory. The (approximate) results indicate that the deviation from Lorentz contraction in this model is, if not zero, very small.