Perturbation theory in the invariant subspace

TL;DR

This paper explores the properties of perturbation theory within invariant subspaces, focusing on the unitary transformation of path-integral measures and their dependence on topological features of phase spaces.

Contribution

It introduces a detailed analysis of perturbation theory in phase space variables and derives the measure in cylindrical coordinates, highlighting topological influences.

Findings

Unitary transformation of path-integral measure described

Properties of perturbation theory in phase space analyzed

Measure in cylindrical coordinates derived

Abstract

The unitary transformation of path-integral differential measure is described. The main properties of perturbation theory in the phase space of action-angle, energy-time variables are investigated. The measure in cylindrical coordinates is derived also. The dependence of perturbation theory contributions from global (topological) properties of corresponding phase spaces is shown.