Classical and quantum dynamics in transverse geometry of Riemannian foliations

TL;DR

This paper surveys classical and quantum dynamics related to transverse Dirac operators on Riemannian foliations, illustrating key results with examples involving fibered and linear foliations on tori.

Contribution

It provides a comprehensive survey of dynamical systems associated with transverse Dirac operators on Riemannian foliations, including illustrative examples.

Findings

Analysis of classical and quantum systems on Riemannian foliations

Examples demonstrating fibered and linear foliations on tori

Insights into transverse Dirac operator dynamics

Abstract

First, we survey some results on classical and quantum dynamical systems associated with transverse Dirac operators on Riemannian foliations. Then we illustrate these results by two examples of Riemannian foliations: a foliation given by the fibers of a fibration and a linear foliation on the two-dimensional torus.