Relativistic Moduli Space for Kink Collisions

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 apparent (coordinate) singularities order-by-order, and systematically incorporates relativistic corrections perturbatively in multi-soliton scattering. It gives an excellent description of kink-antikink collisions in φ 4 field theory already at first order.