Perelomov type coherent states of SO(D + 1) in all dimensional loop quantum gravity

Abstract

A comprehensive study of the application of SO$(D+1)$ coherent states of Perelomov type to loop quantum gravity in general spacetime dimensions $D+1\ge 3$ is given in this paper. We focus on so-called simple representations of SO$(D+1)$ which solve the simplicity constraint and the associated homogeneous harmonic function spaces. With the harmonic function formulation, we study general properties of the coherent states such as the peakedness properties and the inner product. We also discuss the properties of geometric operators evaluated in the coherent states. In particular, we calculate the expectation value of the volume operator, and the results agree with the ones obtained from the classical label of the coherent states up to error terms which vanish in the limit of large representation labels $N$, i.e. the analogue of the large spin limit in standard $3+1$-dimensional loop quantum gravity.

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Cited by in corpus (9)

• Polytopes in all dimensional loop quantum gravity
• Superposition type coherent states in all dimensional loop quantum gravity
• Geometric parametrization of $SO(D+1)$ phase space of 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
• 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
• A note on coarse graining and group representations