Relativistic Moduli Space for Kink Collisions

The moduli space approximation to kink dynamics permits a relativistic generalization if the Derrick scaling parameter is used as a collective coordinate. We develop a perturbative approach to the resulting relativistic moduli space by expanding the Derrick scaling parameter about unity and treating the higher-order Derrick modes as new degrees of freedom. This approach allows us to resolve (coordinate) singularities order-by-order, and systematically incorporates relativistic corrections {\it perturbatively} in kink scattering. It gives an excellent description of kink-antikink collisions in $\phi^4$ field theory already at first order, and at higher order, reproduces the fractal structure in the formation of the final state with an error of only $4\%$.