The Spin-Foam Approach to Quantum Gravity

Pérez, Alejandro

doi:10.12942/lrr-2013-3

Cited by 546 publications

(741 citation statements)

References 400 publications

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“…For the graph F these nodes are expanded into three-valent nodes. Thus a B 2 basis can be identified as a quantum deformed spin network basis [18,51,52,[72][73][74]. This allows us to define a (Ashtekar-Lewandowski like) vacuum state (on a fixed triangulation), by assigning only trivial labels also for the under-crossing graph F u in the B 2 basis.…”

Section: Jhep05(2017)123mentioning

confidence: 99%

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

Dittrich

2017

J. High Energ. Phys.

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We apply the recently suggested strategy to lift state spaces and operators for (2 + 1)-dimensional topological quantum field theories to state spaces and operators for a (3 + 1)-dimensional TQFT with defects. We start from the (2 + 1)-dimensional TuraevViro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects.This work has important applications for quantum gravity as well as the theory of topological phases in (3 + 1) dimensions. It provides a self-dual quantum geometry realization based on a vacuum state peaked on a homogeneously curved geometry. The state spaces and operators we construct here provide also an improved version of the Walker-Wang model, and simplify its analysis considerably.We in particular show that the fusion bases of the (2 + 1)-dimensional theory lead to a rich set of bases for the (3 + 1)-dimensional theory. This includes a quantum deformed spin network basis, which in a loop quantum gravity context diagonalizes spatial geometry operators. We also obtain a dual curvature basis, that diagonalizes the Walker-Wang Hamiltonian.Furthermore, the construction presented here can be generalized to provide state spaces for the recently introduced dichromatic four-dimensional manifold invariants.

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Section: Jhep05(2017)123mentioning

confidence: 99%

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

Dittrich

2017

J. High Energ. Phys.

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“…According to this view the geometric quantum numbers (the spin labels) colouring spin networks seem to be small. On the other hand, investigations in the context of spin foams [34] indicate that the basic building blocks of quantum geometry admit a classical geometric interpretation when coloured by large spins. Moreover, it is in the large spin limit where spin foam amplitudes can be related to general relativity (via a Regge regularization) in the semiclassical regime [32,33].…”

Section: Matter Vs Geometrymentioning

confidence: 99%

Statistics, holography, and black hole entropy in loop quantum gravity

2014

Self Cite

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In loop quantum gravity the quantum states of a black hole horizon are produced by point-like discrete quantum geometry excitations (or punctures) labelled by spin j. The excitations possibly carry other internal degrees of freedom also, and the associated quantum states are eigenstates of the area A operator. On the other hand, the appropriately scaled area operator A/(8π ) is also the physical Hamiltonian associated with the quasilocal stationary observers located at a small distance from the horizon. Thus, the local energy is entirely accounted for by the geometric operator A. We assume that:1. In a suitable vacuum state with regular energy momentum tensor at and close to the horizon the local temperature measured by stationary observers is the Unruh temperature and the degeneracy of 'matter' states is exponential with the area exp (λA/ 2 p )-this is supported by the well established results of QFT in curved spacetimes, which do not determine λ but asserts an exponential behaviour.2. The geometric excitations of the horizon (punctures) are indistinguishable.3. In the semiclassical limit the area of the black hole horizon is large in Planck units. It follows that:1. Up to quantum corrections, matter degrees of freedom saturate the holographic bound, viz.λ must be equal to 1 4 .2. Up to quantum corrections, the statistical black hole entropy coincides with Bekenstein-3. The number of horizon punctures goes like N ∝ A/ 2 p , i.e. the number of punctures N remains large in the semiclassical limit. We also show how the present model (constructed from loop quantum gravity) provides a regularization of (and gives a concrete meaning to) the formal Gibbons-Hawking euclidean path-integral 2 treatment of the black hole system. These results offer a new scenario for semiclassical consistency of loop quantum gravity in the context of black hole physics, and suggest a concrete dynamical mechanism for large spin domination leading simultaneously to semiclassicality and continuity.

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“…This vacuum is a solution of a topological field theory known as BF theory and describes in lattice gauge theory the weak coupling limit. BF theory plays also an important role in the gravity context: it is itself a formulation of (2 + 1) dimensional gravity, and moreover, in (3 + 1) dimensions, it is the starting point for the construction of spin-foam models, a covariant version of loop quantum gravity [47]. A quantum deformed version [28], based on the Turaev-Viro topological theory 8 [48], describing (2 + 1) dimensional Euclidean gravity with positive cosmological constant, is more directly formulated as an extended topological field theory.…”

Section: Jhep02(2017)061mentioning

confidence: 99%

Fusion basis for lattice gauge theory and loop quantum gravity

Delcamp

Dittrich

Riello

2017

J. High Energ. Phys.

133

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We introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2 + 1) dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin-network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel'd double of the gauge group, and can be readily "fused" together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi-local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse-graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin-network basis, in which it is much more complicated to account for electric excitations, i.e. for Gauß constraint violations, emerging at larger scales. Moreover, since the fusion basis comes equipped with a hierarchical structure, it readily provides the language to design states with sophisticated multi-scale structures. Another way to employ this hierarchical structure is to encode a notion of subsystems for lattice gauge theories and (2 + 1) gravity coupled to point particles. In a follow-up work, we have exploited this notion to provide a new definition of entanglement entropy for these theories.

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The Spin-Foam Approach to Quantum Gravity

Cited by 546 publications

References 400 publications

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

Statistics, holography, and black hole entropy in loop quantum gravity

Fusion basis for lattice gauge theory and loop quantum gravity

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