Relativistic moduli space and critical velocity in kink collisions

One important tool in the analysis of the collision of kinks and other topological solitons is the reduction of the original field theory to a finite-dimensional system of so-called collective coordinates. Here we study one recent proposal of a collective coordinate model (CCM), the perturbative relativistic moduli space (pRMS), where the amplitudes of the Derrick modes are promoted to collective coordinates. In particular, we analyze the possibility to calculate within the pRMS the critical velocity, i.e., the initial velocity of kinks at which single bounce scattering changes into a multibounce or annihilation collision. We find that for a growing number of Derrick modes the critical velocity of the CCM approaches the full field theory value. In particular, in the case of the ϕ^{4} model we reach a 99% accuracy. We also see this convergence for a wide range of models belonging to the family of the double sine-Gordon and Christ-Lee theories, especially in those cases where the kinks do not reveal a too well-pronounced half-kink inner structure.