Action-Angle Variables for Complex Projective Space and Semiclassical Exactness

TL;DR

This paper constructs action-angle variables for an integrable model on complex projective space and demonstrates that the semiclassical propagator derived from these variables exactly matches the quantum propagator, revealing a rare case of semiclassical exactness.

Contribution

It introduces a method to explicitly construct action-angle variables for a classical integrable system on complex projective space and proves semiclassical exactness of the propagator.

Findings

Semiclassical propagator coincides with the exact quantum propagator.

Explicit construction of action-angle variables on complex projective space.

Demonstration of semiclassical exactness in this integrable model.

Abstract

We construct the action-angle variables of a classical integrable model defined on complex projective phase space and calculate the quantum mechanical propagator in the coherent state path integral representation using the stationary phase approximation. We show that the resulting expression for the propagator coincides with the exact propagator which was obtained by solving the time-dependent Schr\"odinger equation.