Expansion in the Width and Collective Dynamics of a Domain Wall

TL;DR

This paper develops a new expansion method to analyze the collective dynamics of curved domain walls in a relativistic scalar field model, incorporating higher-order corrections and deriving local equations of motion.

Contribution

It introduces a reformulated expansion in the width of domain walls and derives local equations of motion including third and fourth order corrections.

Findings

Derived Nambu-Goto membrane representation of domain wall dynamics

Included higher-order corrections to the domain wall solution

Obtained a local equation of motion for the domain wall core

Abstract

We show that collective dynamics of a curved domain wall in a (3+1)-dimensional relativistic scalar field model is represented by Nambu-Goto membrane and (2+1)-dimensional scalar fields defined on the worldsheet of the membrane. Our argument is based on a recently proposed by us version of the expansion in the width. Derivation of the expansion is significantly reformulated for the present purpose. Third and fourth order corrections to the domain wall solution are considered. We also derive an equation of motion for the core of the domain wall. Without the (2+1)-dimensional scalar fields this equation would be nonlocal.