Spinfoams near a classical curvature singularity

Huang

2017

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The simplicity constraint is studied in the context of 4d spinfoam models with cosmological constant. We find that the quantum simplicity constraint is realized as the 2d surface defect in SL(2, C) Chern-Simons theory in the construction of spinfoam amplitudes. By this realization of simplicity constraint in Chern-Simons theory, we are able to construct the new spinfoam amplitude with cosmological constant for arbitrary simplicial complex (with many 4-simplices). The semiclassical asymptotics of the amplitude is shown to reproduce correctly the 4-dimensional Einstein-Regge action with cosmological constant term.

Section: Introductionsupporting

confidence: 52%

Loop quantum gravity simplicity constraint as surface defect in complex Chern-Simons theory

Huang

2017

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“…This regime has been studied as the semiclassical regime of LQG from several different perspectives [37][38][39][40][41]. Therefore it is clear that we should consider the gluing of a large number polyhedra p to obtain Σ.…”

Section: Coarse Grained Spin-networkmentioning

confidence: 99%

Loop quantum gravity, exact holographic mapping, and holographic entanglement entropy

Hung

2017

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The relation between Loop Quantum Gravity (LQG) and tensor network is explored from the perspectives of bulk-boundary duality and holographic entanglement entropy. We find that the LQG spinnetwork states in a space Σ with boundary ∂Σ is an exact holographic mapping similar to the proposal in [1]. The tensor network, understood as the boundary quantum state, is the output of the exact holographic mapping emerging from a coarse graining procedure of spin-networks. Furthermore, when a region A and its complementĀ are specified on the boundary ∂Σ, we show that the boundary entanglement entropy S (A) of the emergent tensor network satisfies the Ryu-Takayanagi formula in the semiclassical regime, i.e. S (A) is proportional to the minimal area of the bulk surface attached to the boundary of A in ∂Σ.

“…Among many important achievements of LQG, one of the most profound physical predictions is the resolution of singularities by quantum effects e.g. [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. It is well-known that the classical theory of Einstein gravity breaks down at singularities, while the purpose of quantum gravity is to extend the gravity theory to describe the physics of singularities.…”

mentioning

confidence: 99%

Effective dynamics from coherent state path integral of full loop quantum gravity

Liu

2020

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A new routine is proposed to relate Loop Quant Cosmology (LQC) to Loop Quantum Gravity (LQG) from the perspective of effective dynamics. We derive the big-bang singularity resolution and big bounce from the first principle of full canonical LQG. Our results are obtained in the framework of the reduced phase space quantization of LQG. As a key step in our work, we derive with coherent states a new discrete path integral formula of the transition amplitude generated by the physical Hamiltonian. The semiclassical approximation of the path integral formula gives an interesting set of effective equations of motion (EOMs) for full LQG. When solving the EOMs with homogeneous and isotropic ansatz, we reproduce the LQC effective dynamics in µ 0 -scheme. The solution replaces the big-bang singularity by a big bounce. In the end, we comment on the possible relation between theμ-scheme of effective dynamics and the continuum limit of the path integral formula. arXiv:1910.03763v2 [gr-qc] 23 Dec 20191 The result is also valid in the case of an infinite space. 2 E(γ) and V(γ) denote the set of edges and vertices in γ.