Some novel considerations about the collective coordinates approximation for the scattering of ${\varphi }^4$ kinks

The collective coordinates approximation for the kink/anti-kink scattering in the $1+1$ dimensional ${\varphi }^4$ model is considered and we discuss how the results found in the current literature on the topic can be improved by giving the analytical expression for the lagrangian in the space of parameters. A comprehensive discussion of the role of the collective coordinates approximation in this particular situation is given for completeness.