Higher orders of perturbation theory in the neighborhood of a classical solution

Conclusions

The approach of [1], which is based on direct solution of the Cauchy problem by perturbation theory, is distinguished by the maximal simplicity, and this permits a large body of calculations to be made. As a result of this, we have succeeded in taking into account systematically all the quantum effects in the higher orders and we have for the first time obtained an expression (23) for the mass operator of the system corresponding to the real physical picture. The appearance of the operator arguments of the field (16) indicates a similarity between the approach and the methods of [2,3]. At the same time, our approach has the important advantage that it can be readily extended to the case of (3+1)-dimensional systems, for which the operator arguments of the field cannot be guessed in advance and the approaches of [2,3] are not valid. Problems of this type will be the subject of further investigations.