Action-angle variables in curved space-time

TL;DR

This paper develops a relativistic, curved space version of action-angle variables for particles in gravitational and electromagnetic fields, exemplified by AdS space, and derives semiclassical energy quantization.

Contribution

It introduces a novel formulation of action-angle variables in curved spacetime and applies it to AdS backgrounds, including semiclassical energy quantization.

Findings

Constructed relativistic action-angle variables in curved spacetime.

Applied the framework to particles in AdS space.

Derived semiclassical energy levels for the system.

Abstract

We construct a relativistic and curved space version of action- angle variables for a particle trapped in a gravity and electromagnetic background with time-like isometry. As an example, we consider a particle in AdS background. Furthermore, we obtain the semiclassical quantisation of its energy levels.