  The investigation of the q deformation of the S-matrix for excitations on the
string world sheet in AdS5 x S5 is continued. We argue that due to the lack of
Lorentz invariance the situation is more subtle than in a relativistic theory
in that the nature of bound states depends on their momentum. At low enough
momentum |p|<E the bound states transform in the anti-symmetric representation
of the super-algebra symmetry and become the solitons of the Pohlmeyer reduced
theory in the relativistic limit. At a critical momentum |p|=E they become
marginally unstable, and at higher momenta the stable bound states are in the
symmetric representation and become the familiar magnons in the string limit as
q->1. This subtlety fixes a problem involving the consistency of crossing
symmetry with the relativistic limit found in earlier work. With mirror
kinematics, obtained after a double Wick rotation, the bound state structure is
simpler and there are no marginally unstable bound states.
