Classical and Quantum Dynamics on Orbifolds

TL;DR

This paper extends the Egorov theorem to orbifolds, addressing both classical and noncommutative geometric perspectives, enhancing understanding of quantum-classical correspondence on singular spaces.

Contribution

It introduces two versions of the Egorov theorem tailored for orbifolds, bridging classical and noncommutative geometric frameworks.

Findings

Extended Egorov theorem for orbifolds as smooth spaces

Egorov theorem for orbifolds as singular spaces via noncommutative geometry

Provides tools for quantum dynamics on orbifolds

Abstract

We present two versions of the Egorov theorem for orbifolds. The first one is a straightforward extension of the classical theorem for smooth manifolds. The second one considers an orbifold as a singular manifold, the orbit space of a Lie group action, and deals with the corresponding objects in noncommutative geometry.