Relativistic moduli space for kink collisions
C. Adam, N. S. Manton, K. Oleś, T. Romańczukiewicz, A. Wereszczyński
Abstract
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 perturbatively in kink scattering. It gives an excellent description of kink-antikink collisions in ${\ensuremath{\phi}}^{4}$ 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%.