Semi-classical States in Homogeneous Loop Quantum Cosmology

TL;DR

This paper constructs and analyzes semi-classical states in homogeneous loop quantum cosmology using two methods, demonstrating their classical limit and mathematical properties.

Contribution

It introduces two novel approaches to construct semi-classical states in homogeneous LQC and verifies their correct classical limit behavior.

Findings

Hamiltonian constraint has the correct classical limit with these states

Coherent states are successfully constructed via two different methods

Semi-classical states facilitate the analysis of quantum dynamics in LQC

Abstract

Semi-classical states in homogeneous loop quantum cosmology (LQC) are constructed by two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semi-classical (coherent) state is obtained by solving the eigen-equation of that operator. Moreover, we use these coherent states to analyze the semi-classical limit of the quantum dynamics. It turns out that the Hamiltonian constraint operator employed currently in homogeneous LQC has correct classical limit with respect to the coherent states. In the second approach, the other kind of semi-classical state is derived from the mathematical construction of coherent states for compact Lie groups due to Hall.