Discrete evolution for the zero-modes of the Quantum Liouville Model

TL;DR

This paper investigates the discrete evolution of zero modes in the quantum Liouville model, focusing on the structure of the modular double in the quantum case and its implications for the dynamics.

Contribution

It introduces the structure of the modular double in the quantum case and analyzes the discrete evolution of zero modes in the Liouville model.

Findings

Characterization of the discrete evolution for zero modes.

Introduction of the modular double structure in the quantum case.

Insights into the dynamics of the quantum Liouville model.

Abstract

The dynamical system for the zero modes of the Liouville Model, which is separated from the full dynamics for the discrete shifts of time $ t \to t + \pi $, is investigated. The structure of the modular double in quantum case is introduced.