Superposition type coherent states in all dimensional loop quantum gravity

Abstract

We propose a new kind of coherent state for the general $SO(D+1)$ formulation of loop quantum gravity in the $(1+D)$-dimensional space-time. Instead of Thiemann's coherent state for $SO(D+1)$ gauge theory, our coherent spin-network state is given by constructing proper superposition over quantum numbers of the spin-networks with vertices labelled by the coherent intertwiners. Such superposition type coherent states are labelled by the so-called generalized twisted geometric variables which capture the geometric meaning of discretized general relativity. We study the basic properties of this kind of coherent states, i.e., the completeness and peakedness property. Moreover, we show that the superposition type coherent states are consistent with Thiemann's coherent state for $SO(D+1)$ gauge theory in large $\eta$ limit.

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Cited by in corpus (8)

• Higher-dimensional quantum Oppenheimer-Snyder model
• Polytopes in all dimensional loop quantum gravity
• Twisted geometry coherent states in all dimensional loop quantum gravity: I. Construction and Peakedness properties
• The thermodynamics of isolated horizons in loop quantum gravity
• The effective dynamics of weak coupling loop quantum gravity
• Spin foam amplitude of the black-to-white hole transition
• 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