Relational evolution of a simple quantum Hamiltonian model

TL;DR

This paper investigates the quantum and classical dynamics of a reparametrization-invariant system with zero Hamiltonian, using an internal time parameter and the Pegg-Barnett phase operator to describe relational evolution.

Contribution

It introduces a novel approach to describe relational quantum dynamics using the Pegg-Barnett phase operator in finite-dimensional Hilbert spaces.

Findings

Successful construction of an internal time parameter for the system

Application of Pegg-Barnett phase operator in quantum relational dynamics

Insights into classical and quantum evolution of reparametrization-invariant systems

Abstract

We study the quantum dynamics of a time reparametrization invariant system with a vanishing Hamiltonian. The evolution of the physical degrees of freedom of the system is described, both at the classical and at the quantum level, in relational terms by the construction of an internal time parameter. We use the Pegg-Barnett phase operator formalism in finite dimensional Hilbert space as an essential ingredient.