Collective coordinate model of kink-antikink collisions in $\phi^4$ theory

TL;DR

This paper introduces a collective coordinate model for kink-antikink collisions in $^4$ theory, capturing the fractal velocity patterns through effective moduli and regularizing previous mathematical issues.

Contribution

It presents a novel dynamical model with two effective moduli that accurately reproduces complex collision patterns in $^4$ theory.

Findings

The model reproduces fractal velocity patterns.

The shape mode approximates Lorentz contractions.

Null-vector issues at zero separation are resolved.

Abstract

The fractal velocity pattern in symmetric kink-antikink collisions in $\phi^4$ theory is shown to emerge from a dynamical model with two effective moduli, the kink-antikink separation and the internal shape mode amplitude. The shape mode usefully approximates Lorentz contractions of the kink and antikink, and the previously problematic null-vector in the shape mode amplitude at zero separation is regularized.