Loop expansion and the bosonic representation of loop quantum gravity

Bianchi, Eugenio; Guglielmon, Jonathan; Hackl, Lucas; Yokomizo, Nelson

doi:10.1103/physrevd.94.086009

Cited by 26 publications

(49 citation statements)

References 47 publications

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“…When compared to our numerical data, we find good agreement within our approximation. The expectation that entanglement in the degrees of freedom of the gravitational field is a necessary condition for the emergence of a classical spacetime is shared by various approaches to nonperturbative quantum gravity [26][27][28][29][30][31][32][33][34]. The result that Bell-network states satisfy an area law supports the conjecture that entanglement can be used as a probe of semiclassicality in quantum gravity [28].…”

Section: )mentioning

confidence: 86%

“…Moreover, we can require correlations between two adjacent quantum polyhedra so that also the fluctuations of the shape of two adjacent faces are correlated. Bell-network states [20,31,32] are a specific proposal that uniformly maximizes correlations of all neighboring polyhedra on a given graph. They are given by the formula…”

Section: Bell-network States and Vector Geometriesmentioning

confidence: 99%

“…Given a graph Γ, the Hilbert space of a link ∈ Γ can be thought of as the Hilbert space of four harmonic oscillators, two at the source and two at the target of the link [32]. Denoting the creation operators a † s α and a † t α , where α = 1, 2 is a spinor index, we build a Bell state of the link as…”

Section: Bell-network States and Vector Geometriesmentioning

confidence: 99%

See 2 more Smart Citations

Entanglement entropy of Bell-network states in loop quantum gravity: Analytical and numerical results

2019

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Bell-network states are loop-quantum-gravity states that glue quantum polyhedra with entanglement. We present an algorithm and a code that evaluates the reduced density matrix of a Bell-network state and computes its entanglement entropy. In particular, we use our code for simple graphs to study properties of Bell-network states and to show that they are non-typical in the Hilbert space. Moreover, we investigate analytically Bell-network states on arbitrary finite graphs. We develop methods to compute the Rényi entropy of order p for a restriction of the state to an arbitrary region. In the uniform large-spin regime, we determine bounds on the entanglement entropy and show that it obeys an area law. Finally, we discuss the implications of our results for correlations of geometric observables.

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Section: )mentioning

confidence: 86%

Section: Bell-network States and Vector Geometriesmentioning

confidence: 99%

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Entanglement entropy of Bell-network states in loop quantum gravity: Analytical and numerical results

2019

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“…Therefore the contributing of J iν in F 2 is seen in the holonomy T r (U (γ, A)). In bosonic representation of loop quantum gravity, the holonomy is given by [23] (…”

Section: So the Equation Of Motion For ωmentioning

confidence: 99%

Yang–Mills Theory of Gravity

Matwi¹

2019

Physics

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The canonical formulation of general relativity (GR) is based on decomposition space–time manifold M into R × Σ , where R represents the time, and Ksi is the three-dimensional space-like surface. This decomposition has to preserve the invariance of GR, invariance under general coordinates, and local Lorentz transformations. These symmetries are associated with conserved currents that are coupled to gravity. These symmetries are studied on a three dimensional space-like hypersurface Σ embedded in a four-dimensional space–time manifold. This implies continuous symmetries and conserved currents by Noether’s theorem on that surface. We construct a three-form E i ∧ D A i (D represents covariant exterior derivative) in the phase space ( E i a , A a i ) on the surface Σ , and derive an equation of continuity on that surface, and search for canonical relations and a Lagrangian that correspond to the same equation of continuity according to the canonical field theory. We find that Σ i 0 a is a conjugate momentum of A a i and Σ i a b F a b i is its energy density. We show that there is conserved spin current that couples to A i , and show that we have to include the term F μ ν i F μ ν i in GR. Lagrangian, where F i = D A i , and A i is complex S O ( 3 ) connection. The term F μ ν i F μ ν i includes one variable, A i , similar to Yang–Mills gauge theory. Finally we couple the connection A i to a left-handed spinor field ψ , and find the corresponding beta function.

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“…Similarly to what happens for spins, gluing the adjacent faces of two neighboring quantum polyhedra requires entanglement. In this paper we use the formalism of squeezed spinnetworks [21,22] to build entangled states for neighboring quantum polyhedra. The idea can be illustrated by focusing on a single link of the spin-network graph.…”

Section: Introductionmentioning

confidence: 99%

Gluing polyhedra with entanglement in loop quantum gravity

2018

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In a spin-network basis state, nodes of the graph describe un-entangled quantum regions of space, quantum polyhedra. In this paper we show how entanglement between intertwiner degrees of freedom enforces gluing conditions for neighboring quantum polyhedra. In particular we introduce Bell-network states, entangled states defined via squeezed vacuum techniques. We study correlations of quantum polyhedra in a dipole, a pentagram and a generic graph. We find that vector geometries, structures with neighboring polyhedra having adjacent faces glued back-to-back, arise from Bell-network states. We also discuss the relation to Regge geometries. The results presented show clearly the role that entanglement plays in the gluing of neighboring quantum regions of space.

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Loop expansion and the bosonic representation of loop quantum gravity

Cited by 26 publications

References 47 publications

Entanglement entropy of Bell-network states in loop quantum gravity: Analytical and numerical results

Entanglement entropy of Bell-network states in loop quantum gravity: Analytical and numerical results

Yang–Mills Theory of Gravity

Gluing polyhedra with entanglement in loop quantum gravity

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