Fields topology and perturbation theory

TL;DR

This paper introduces a novel perturbation theory framework for quantum fields using a unitary transformation in a space of collective variables, with applications demonstrated in quantum mechanics and field theory.

Contribution

It presents a new form of perturbation theory based on unitary mapping in a collective variable space, enhancing the analysis of quantum field dynamics.

Findings

Perturbation contributions can be accumulated exactly on the boundary of the collective variable space.

The formalism is applicable to quantum mechanics and field theory examples.

The approach offers a new perspective on fields topology and nonlinear modes quantization.

Abstract

The fields nonlinear modes quantization scheme is discussed. New form of the perturbation theory achieved by unitary mapping the quantum dynamics in the space $W_G$ of (action, angle)-type collective variables. It is shown why the transformed perturbation theory contributions may accumulated exactly on the boundary $\pa W_G$. Abilities of the developed formalism are illustrated by examples from quantum mechanics and field theory.