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

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 $\hslash$, the values of the corresponding classical functions at the twisted geometry space point where the coherent state is peaked.

References in corpus (13)

• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• Polyhedra in loop quantum gravity
• Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
• Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• Revisiting the Simplicity Constraints and Coherent Intertwiners
• First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian
• Superposition type coherent states in all dimensional loop quantum gravity
• Twisted geometry coherent states in all dimensional loop quantum gravity: I. Construction and Peakedness properties
• The effective dynamics of weak coupling loop quantum gravity

Cited by in corpus (2)

• The thermodynamics of isolated horizons in loop quantum gravity
• On the gauge reduction with respect to simplicity constraint in all dimensional loop quantum gravity