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

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.