Twisted geometry coherent states in all dimensional loop quantum gravity: II. Ehrenfest Property

TL;DR

This paper proves that twisted geometry coherent states in all dimensional loop quantum gravity accurately reproduce classical values of observables at the quantum state's peak, confirming their semiclassical consistency.

Contribution

It establishes the Ehrenfest property for these coherent states, demonstrating their semiclassical behavior in all dimensions within loop quantum gravity.

Findings

Expectation values match classical functions at the peaked point

Coherent states exhibit the Ehrenfest property in all dimensions

Supports their use as semiclassical states in quantum gravity

Abstract

In the preceding paper of this series of articles we constructed the twisted geometry coherent states in all dimensional loop quantum gravity and established their peakedness properties. In this paper we establish the "Ehrenfest property" of these coherent states which are labelled by the twisted geometry parameters. By this we mean that the expectation values of the polynomials of the elementary operators as well as the operators which are not polynomial functions of the elementary operators, reproduce, to zeroth order in $\hbar$, the values of the corresponding classical functions at the twisted geometry space point where the coherent state is peaked.