The canonical quantization of the kink -- model beyond the static solution

TL;DR

This paper introduces a novel quantization method for the relativistic kink model using collective coordinates, resulting in an effective action that reproduces the known spectrum of the kink solution.

Contribution

It develops a new collective coordinates approach for quantizing the relativistic kink, linking it to a nonminimal point-particle action with curvature.

Findings

Effective action corresponds to a nonminimal $d=1+1$ point-particle with curvature.

Canonical quantization reproduces the kink spectrum obtained by WKB methods.

Provides a new framework for quantizing solitonic solutions in relativistic models.

Abstract

A new approach to the quantization of the relativistic kink - model around the solitonic solution is developed on the ground of the collective coordinates method. The corresponding effective action is proved to be the action of the nonminimal $d=1+1$ point - particle with curvature. It is shown that upon canonical quantization this action yields the spectrum of kink - solution obtained firstly with the help of the WKB - quantization.