Heisenberg fields in the neighborhood of a classical solution

Abstract

For the example of nonlinear models of a scalar field in two-dimensional space-time a study is made of a method of quantization in the neighborhood of a classical solution based on direct solution by perturbation theory of the Cauchy problem for the Heisenberg field equations. It is shown that, as in the classical Bogolyubov-Krylov method, zero modes and associated secular terms arise because of the perturbation-theory expansion of the Bogolyubov operator argument of the classical component. The Lehmann-Symanzik-Zimmermann procedure is used to make a complete investigation of the asymptotic states of the field in the soliton sector in the lowest orders of perturbation theory.