Quantization of a soliton solution in a (3+1)-dimensional model of a scalar field with self-interaction involving derivatives

A soliton soliton is constructed in (3+1)-dimensional scalar field model with self-interaction including derivatives. Quantization of this solution is carried out by means of the direct perturbalive solution of quantum Cauchy's problem for Heisenberg field equation. Zero modes are shown to appear as a result of the perturbative expansion of Bogoliubov's operator-valued argument of the classical component. They can be taken into account by introducing corresponding corrections to this argument. With the help of LSZ procedure an investigation of the interaction between the soliton and secondary field quanta is carried out.