Asymptotics of 4d spin foam models

Barrett, John W.; Dowdall, Richard J.; Fairbairn, Winston J.; Gomes, Henrique; Hellmann, Frank; Pereira, Roberto

doi:10.1007/s10714-010-0983-7

Cited by 33 publications

(61 citation statements)

References 31 publications

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“…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]. From the present analysis of Section II B 1-equations (32) and (33)-we find…”

Section: Matter Vs Geometrymentioning

confidence: 65%

“…It rather follows from the semi-classical approximation. Since (as argued before) in our case large spins dominate (analogue of the semiclassical approximation), we expect that the semiclassical approximation of the spin foam transition amplitudes [32,33] would provide a rigorous implementation of this last formal step. This is related to the ideas put forward in [3] (see version 1 on Arxiv) when exploring the dynamics of a single plaquette (puncture).…”

Section: Semiclassical Consistency: General Relativity Emerging mentioning

confidence: 92%

“…These numbers as well as (32) and (33) are all large in the macroscopic regime and thus, the tension evoked above disappears. Thus, the system is dynamically driven to the configurations one would expect from naive semiclassical and continuum limit considerations.…”

Section: Matter Vs Geometrymentioning

confidence: 93%

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

2014

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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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Section: Matter Vs Geometrymentioning

confidence: 65%

Section: Semiclassical Consistency: General Relativity Emerging mentioning

confidence: 92%

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

2014

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“…With finite group models, it might be in particular possible to access the many-particle (that is many simplices or building blocks in the triangulation) and small-spin (corresponding to small geometrical size of the building blocks) regime. 2 This is in contrast to the few-particle and large-spin (semiclassical) regime [67][68][69] which is accessible so far.…”

Section: Introductionmentioning

confidence: 91%

Spin Foam Models with Finite Groups

2013

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Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity-inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensed-matter systems.

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“…The asymptotics of the Ponzano-Regge model on handlebodies (with more than one tetrahedron) is presented in [23]. Recent works have also focused on more complicated objects, like the 15j-symbol and EPR amplitude in [24,25]. An extended Born-Oppenheimer approximation has been developed and applied to the asymptotics of the 9j, 12j and 15j-symbols with some large and small angular momenta [26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

A New Recursion Relation for the 6j-Symbol

Bonzom

Livine

2011

Ann. Henri Poincaré

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The 6j-symbol is a fundamental object from the re-coupling theory of SU(2) representations. In the limit of large angular momenta, its asymptotics is known to be described by the geometry of a tetrahedron with quantized lengths. This article presents a new recursion formula for the square of the 6j-symbol. In the asymptotic regime, the new recursion is shown to characterize the closure of the relevant tetrahedron. Since the 6j-symbol is the basic building block of the Ponzano-Regge model for pure three-dimensional quantum gravity, we also discuss how to generalize the method to derive more general recursion relations on the full amplitudes.Comment: 10 pages, v2: title and introduction changed, paper re-structured; Annales Henri Poincare (2011

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Asymptotics of 4d spin foam models

Cited by 33 publications

References 31 publications

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

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

Spin Foam Models with Finite Groups

A New Recursion Relation for the 6j-Symbol

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