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

Long, Gaoping

doi:10.1103/physrevd.106.066021

Cited by 3 publications

(5 citation statements)

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“…More explicitly, similar to the construction of twisted geometry coherent state in the solution space of edge simplicity constraint, one could decompose the heat-kernel coherent state of SO(D+1) based on the twisted geometry parametrization for × e∈γ T * ss SO(D+1) e , and then select the terms dominated by the highest and lowest weight in each representation of SO(D + 1), to form the twisted geometry coherent state in the full Hilbert space of all dimensional LQG. This will be the subject of a follow up work [40].…”

Section: Discussionmentioning

confidence: 93%

“…An important application of the twisted geometry parametrization is the construction of the twisted geometry coherent state. Such kind of coherent states is firstly established in SU (2) LQG [26], and then it is generalized to the SO(D + 1) LQG with the restriction of the simple representations [27][28][29][30][31]. Specifically, based on the twisted geometry parameters, the simple twisted geometry coherent state in the strong solution space of quantum edge simplicity constraints is established by selecting the dominant terms (which is referred to as Perelomov type coherent state [25,28,32]) with simple representation of SO(D + 1) in the decomposition of the heat-kernel coherent state of SO(D + 1) [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

“…It has been shown that the simple twisted geometry coherent states take the Gaussian superposition formulations. Especially, the simple twisted geometry coherent states provides an over-complete basis of the strong solution space of quantum edge simplicity constraints, and their wave functions have wellbehaved peakedness and Ehrenfest properties in the reduced phase space with respect to the edge simplicity constraints [30,31].…”

Section: Introductionmentioning

confidence: 99%

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Gauge reduction with respect to simplicity constraint in all dimensional loop quantum gravity

Long

Zhang

2023

Phys. Rev. D

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The regularization of the scalar constraint and the Fermion coupling problem indicate that it is necessary to consider some kind of gauge fixing methods to deal with the simplicity constraint in all dimensional SO(D + 1) loop quantum gravity. The coherent state with wellbehaved peakedness property is an essential ingredient to carry out the gauge fixing method. To provide the basic tool for constructing such kind of coherent state, we generalize the twisted geometry parametrization of the SO(D + 1) holonomy-flux phase space of (1 + D)-dimensional loop quantum gravity from the edge simplicity constraint surface to a dense subspace in the SO(D + 1) holonomy-flux phase space. The symplectic structure on the twisted geometric parameter space and the Poisson structure in terms of the twisted geometric variables are analyzed. Besides, we discuss the relation between the two twisted geometry parametrizations constructed respectively on the edge simplicity constraint surface and the dense subspace of the SO(D+1) holonomy-flux phase space. Our result show that these two type of parametrizations are equivalent to each other by carrying out the gauge reduction with respect to the edge simplicity constraint.

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Section: Discussionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gauge reduction with respect to simplicity constraint in all dimensional loop quantum gravity

Long

Zhang

2023

Phys. Rev. D

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“…LQG and the twisted geometry coherent states in SO(D + 1) LQG are both expected to provide some kind of semi-classical description of the (1 + D)-dimensional spacetime geometry [22][23][24]. Hence, it is worth to compare the properties of these two kinds of coherent states.…”

Section: Discussionmentioning

confidence: 99%

“…By taking specific superpositions of the spin-network states labelled by the simple coherent intertwiners, the coherent states labelled by the twisted geometry parameters can be established, and it has been verified that these coherent states have well-behaved peakedness and Ehrenfest Properties [21][22][23][24] With the Gaussian and simplicity constraints being solved, the spatial geometric operators can be constructed based on the elementary operators in the kinematic physical Hilbert space [25][26][27]. For example, the (D − 1)-area operator reads Ar(S e ) = 2 F IJ e Fe,IJ ,…”

Section: The Hilbert Space and Kinematic Constraintsmentioning

confidence: 95%

The weak coupling theory of all dimensional loop quantum gravity

Long¹,

Lin²

2022

Preprint

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The weak coupling loop quantum theory with Abelian gauge group provides us a new perspective to study the weak coupling properties of LQG. In this paper, the weak coupling theory of all dimensional loop quantum gravity is established based on a symplectic-morphism between the SO(D + 1) holonomy-flux phase space and the U (1)holonomy-flux phase space. More explicitly, the Gaussian, simplicity, diffeomorphism and scalar constraint operators in SO(D + 1) loop quantum gravity will be generalized to the U (1) D(D+1) 2 loop quantum theory based on the symplectic-morphism, and the U (1) D(D+1) 2 loop quantum theory equipped with these constraint operators gives the weak coupling U (1) D(D+1) 2 loop quantum gravity, with the corresponding Hilbert space is composed by the U (1) D(D+1) 2 heat-kernel coherent states which are peaked at the weak coupling region of the U (1) D(D+1) 2 holonomy-flux phase space.

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