Twisted geometry coherent states in all dimensional loop quantum gravity: Construction and peakedness properties

摘要

A new family of coherent states for all dimensional loop quantum gravity is 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 provides an overcomplete 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 semiclassical parameter t. Therefore, this family of coherent states can serve as a candidate for the semiclassical analysis of all dimensional loop quantum gravity.

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