Abstract
We compute metric correlations in loop quantum gravity with the dynamics defined by the new spin foam models. The analysis is done at the lowest order in a vertex expansion and at the leading order in a large spin expansion. The result is compared to the graviton propagator of perturbative quantum gravity.
Highlights
In this paper we compute metric correlations in Loop Quantum Gravity (LQG) [1, 2, 3] and we compare them with the scaling and the tensorial structure of the graviton propagator in perturbative Quantum Gravity [4, 5, 6]
The dynamics is implemented in terms of the new spin foam models introduced by Engle, Pereira, Rovelli and Livine (EPRLγ model) [19] and by Freidel and Krasnov (FKγ model) [20]
The plan of the paper is the following: in section 2 we introduce the metric operator and construct a semiclassical boundary state; in section 3 we recall the form of the new spin foam models; in section 4 we define the LQG propagator and provide an integral formula for it at the lowest order in a vertex expansion; in section 5 we compute its large spin asymptotics; in section 6 we discuss expectation values of metric operators; in section 7 we present our main result: the scaling and the tensorial structure of the LQG propagator at the leading order of our expansion; in section 8 we attempt a comparison with the graviton propagator of perturbative quantum gravity
Summary
In this paper we compute metric correlations in Loop Quantum Gravity (LQG) [1, 2, 3] and we compare them with the scaling and the tensorial structure of the graviton propagator in perturbative Quantum Gravity [4, 5, 6]. The plan of the paper is the following: in section 2 we introduce the metric operator and construct a semiclassical boundary state; in section 3 we recall the form of the new spin foam models; in section 4 we define the LQG propagator and provide an integral formula for it at the lowest order in a vertex expansion; in section 5 we compute its large spin asymptotics; in section 6 we discuss expectation values of metric operators; in section 7 we present our main result: the scaling and the tensorial structure of the LQG propagator at the leading order of our expansion; in section 8 we attempt a comparison with the graviton propagator of perturbative quantum gravity
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