546 research outputs found
Asymptotics of 4d spin foam models
We study the asymptotic properties of four-simplex amplitudes for various
four-dimensional spin foam models. We investigate the semi-classical limit of
the Ooguri, Euclidean and Lorentzian EPRL models using coherent states for the
boundary data. For some classes of geometrical boundary data, the asymptotic
formulae are given, in all three cases, by simple functions of the Regge action
for the four-simplex geometry.Comment: 10 pages, Proceedings for the 2nd Corfu summer school and workshop on
quantum gravity and quantum geometry, talk given by Winston J. Fairbair
A New Recursion Relation for the 6j-Symbol
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
Coupling of spacetime atoms and spin foam renormalisation from group field theory
We study the issue of coupling among 4-simplices in the context of spin foam
models obtained from a group field theory formalism. We construct a
generalisation of the Barrett-Crane model in which an additional coupling
between the normals to tetrahedra, as defined in different 4-simplices that
share them, is present. This is realised through an extension of the usual
field over the group manifold to a five argument one. We define a specific
model in which this coupling is parametrised by an additional real parameter
that allows to tune the degree of locality of the resulting model,
interpolating between the usual Barrett-Crane model and a flat BF-type one.
Moreover, we define a further extension of the group field theory formalism in
which the coupling parameter enters as a new variable of the field, and the
action presents derivative terms that lead to modified classical equations of
motion. Finally, we discuss the issue of renormalisation of spin foam models,
and how the new coupled model can be of help regarding this.Comment: RevTeX, 18 pages, no figure
Quantizing speeds with the cosmological constant
Considering the Barrett-Crane spin foam model for quantum gravity with
(positive) cosmological constant, we show that speeds must be quantized and we
investigate the physical implications of this effect such as the emergence of
an effective deformed Poincare symmetry.Comment: 4 pages, revtex4, 3 figure
Holography in the EPRL Model
In this research announcement, we propose a new interpretation of the EPR
quantization of the BC model using a functor we call the time functor, which is
the first example of a CLa-ren functor. Under the hypothesis that the universe
is in the Kodama state, we construct a holographic version of the model.
Generalisations to other CLa-ren functors and connections to model category
theory are considered.Comment: research announcement. Latex fil
Conditional probabilities in Ponzano-Regge minisuperspace
We examine the Hartle-Hawking no-boundary initial state for the Ponzano-Regge
formulation of gravity in three dimensions. We consider the behavior of
conditional probabilities and expectation values for geometrical quantities in
this initial state for a simple minisuperspace model consisting of a
two-parameter set of anisotropic geometries on a 2-sphere boundary. We find
dependence on the cutoff used in the construction of Ponzano-Regge amplitudes
for expectation values of edge lengths. However, these expectation values are
cutoff independent when computed in certain, but not all, conditional
probability distributions. Conditions that yield cutoff independent expectation
values are those that constrain the boundary geometry to a finite range of edge
lengths. We argue that such conditions have a correspondence to fixing a range
of local time, as classically associated with the area of a surface for
spatially closed cosmologies. Thus these results may hint at how classical
spacetime emerges from quantum amplitudes.Comment: 26 pages including 10 figures, some reorganization in the
presentation of results, expanded discussion of results in the context of 2+1
gravity in the Witten variables, 3 new reference
Dichromatic state sum models for four-manifolds from pivotal functors
A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category.
A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary ribbon fusion category is recovered, including the nonmodular case. It is shown that the Crane-Yetter invariant for nonmodular categories is stronger than signature and Euler invariant.
A special case is the four-dimensional untwisted Dijkgraaf-Witten model. Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models.
Relations to different approaches to quantum gravity such as Cartan geometry and teleparallel gravity are also discussed
Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, Symbols, and Character Localization
In this paper we employ a novel technique combining the Euler Maclaurin
formula with the saddle point approximation method to obtain the asymptotic
behavior (in the limit of large representation index ) of generic Wigner
matrix elements . We use this result to derive asymptotic
formulae for the character of an SU(2) group element and for
Wigner's symbol. Surprisingly, given that we perform five successive
layers of approximations, the asymptotic formula we obtain for is
in fact exact. This result provides a non trivial example of a
Duistermaat-Heckman like localization property for discrete sums.Comment: 36 pages, 3 figure
Note on Global Regularity for 2D Oldroyd-B Fluids with Diffusive Stress
We prove global regularity of solutions of Oldroyd-B equations in 2 spatial
dimensions with spatial diffusion of the polymeric stresses
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