Twisted geometry coherent states in all dimensional loop quantum gravity: I. Construction and Peakedness properties

Abstract

A new family of coherent states for all dimensional loop quantum gravity are proposed, which is based on the generalized twisted geometry parametrization of the phase space of $SO(D+1)$ connection theory. We prove that this family of coherent states provide an over-complete basis of the Hilbert space in which edge simplicity constraint is solved. Moreover, according to our explicit calculation, the expectation values of holonomy and flux operators with respect to this family of coherent states coincide with the corresponding classical values given by the labels of the coherent states, up to some gauge degrees of freedom. Besides, we study the peakedness properties of this family of coherent states, including the peakedness of the wave functions of this family of coherent states in holonomy, momentum and phase space representations. It turns out that the peakedness in these various representations and the (relative) uncertainty of the expectation values of the operators are well controlled by the semi-classical parameter $t$. Therefore, this family of coherent states provide a candidate for the semi-classical analysis of all dimensional loop quantum gravity.

References in corpus (7)

• A new spinfoam vertex for 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
• First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian
• Superposition type coherent states in all dimensional loop quantum gravity
• The effective dynamics of weak coupling loop quantum gravity

Cited by in corpus (4)

• Spin foam amplitude of the black-to-white hole transition
• The thermodynamics of isolated horizons in loop quantum gravity
• Twisted geometry coherent states in all dimensional loop quantum gravity: II. Ehrenfest Property
• On the gauge reduction with respect to simplicity constraint in all dimensional loop quantum gravity