Relativistic Moduli Space for Kink Collisions

TL;DR

This paper develops a perturbative relativistic moduli space approach for kink collisions, improving the accuracy of scattering predictions in $ ext{phi}^4$ theory and capturing complex fractal structures with minimal error.

Contribution

It introduces a systematic perturbative method to incorporate relativistic effects into the moduli space approximation for kink dynamics.

Findings

Accurately describes kink-antikink collisions at first order.

Reproduces fractal scattering structures with only 4% error at higher order.

Provides a systematic way to resolve coordinate singularities in relativistic moduli space.

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 {\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 $4\%$.