Topology and perturbation theory

Abstract

Paper contains description of the fields nonlinear modes successive quantization scheme. It is shown that the path integrals for absorption part of amplitudes are defined on the Dirac ($\d$-like) functional measure. This permits arbitrary transformation of the functional integral variables. New form of the perturbation theory achieved by mapping the quantum dynamics in the space $W_G$ of the ({\it action, angle})-type collective variables. It is shown that the transformed perturbation theory contributions are accumulated exactly on the boundary $\pa W_G$. Abilities of the developed formalism are illustrated by the Coulomb problem. This model is solved in the $W_C$=({\it angle, angular momentum, Runge-Lentz vector}) space and the reason of its exact integrability is `emptiness' of $\pa W_C$.