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Coarse graining methods for spin net and spin foam models,” New J. Phys. 14, 035008 (2012) [arXiv:1109.4927 [grqc
 Holonomy Spin Foam Models: Definition and Coarse Graining,” Phys. Rev. D 87, 044048 (2013) [arXiv:1208.3388 [grqc
"... We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large scale analysis by numerical and computational methods. In particular, we apply MigdalKadanoff and Tensor Network Renormalization schemes to spin net and spin foam models based on fini ..."
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Cited by 20 (11 self)
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We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large scale analysis by numerical and computational methods. In particular, we apply MigdalKadanoff and Tensor Network Renormalization schemes to spin net and spin foam models based on finite Abelian groups and introduce ‘cutoff models ’ to probe the fate of gauge symmetries under various such approximated renormalization group flows. For the Tensor Network Renormalization analysis, a new Gauß constraint preserving algorithm is introduced to improve numerical stability and aid physical interpretation. We
Discrete Gravity Models and Loop Quantum Gravity: a Short Review
, 2012
"... We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the Plebanski action. We discuss the role of discrete geometries in the ..."
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Cited by 6 (0 self)
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We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the Plebanski action. We discuss the role of discrete geometries in the spin foam formalism, with particular attention to the definition of the simplicity constraints.
Topological lattice field theories from intertwiner dynamics,” arXiv:1311.1798 [grqc
"... We introduce a class of 2D lattice models that describe the dynamics of intertwiners, or, in a condensed matter interpretation, the fusion and splitting of anyons. We identify different families and instances of triangulation invariant, that is, topological, models inside this class. These models gi ..."
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We introduce a class of 2D lattice models that describe the dynamics of intertwiners, or, in a condensed matter interpretation, the fusion and splitting of anyons. We identify different families and instances of triangulation invariant, that is, topological, models inside this class. These models give examples for symmetry protected topologically ordered 1D quantum phases with quantum group symmetries. Furthermore the models provide realizations for anyon condensation into a new effective vacuum. We explain the relevance of our findings for the problem of identifying the continuum limit of spin foam and spin net models. 1
The Construction of Spin Foam Vertex Amplitudes ⋆
"... Abstract. Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. These fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a 4dimensional generalization of the Ponzano–Regge m ..."
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Abstract. Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. These fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a 4dimensional generalization of the Ponzano–Regge model for 3d quantum gravity. We motivate and review the construction of the vertex amplitudes of recent spin foam models, giving two different and complementary perspectives of this construction. The first proceeds by extracting geometric configurations from a topological theory of the BF type, and can be seen to be in the tradition of the work of Barrett, Crane, Freidel and Krasnov. The second keeps closer contact to the structure of Loop Quantum Gravity and tries to identify an appropriate set of constraints to define a Lorentzinvariant interaction of its quanta of space. This approach is in the tradition of the work of Smolin, Markopoulous, Engle, Pereira, Rovelli and Livine. Key words: spin foam models; discrete quantum gravity; generalized lattice gauge theory 2010 Mathematics Subject Classification: 81T25; 81T45 1
Asymptotic Analysis of the Ponzano–Regge Model with NonCommutative Metric Boundary Data?
"... Abstract. We apply the noncommutative Fourier transform for Lie groups to formulate the noncommutative metric representation of the Ponzano–Regge spin foam model for 3d quantum gravity. The noncommutative representation allows to express the amplitudes of the model as a first order phase space pa ..."
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Abstract. We apply the noncommutative Fourier transform for Lie groups to formulate the noncommutative metric representation of the Ponzano–Regge spin foam model for 3d quantum gravity. The noncommutative representation allows to express the amplitudes of the model as a first order phase space path integral, whose properties we consider. In particular, we study the asymptotic behavior of the path integral in the semiclassical limit. First, we compare the stationary phase equations in the classical limit for three different noncommutative structures corresponding to the symmetric, Duflo and Freidel–Livine–Majid quantization maps. We find that in order to unambiguously recover discrete geometric constraints for noncommutative metric boundary data through the stationary phase method, the deformation structure of the phase space must be accounted for in the variational calculus. When this is understood, our results demonstrate that the noncommutative metric representation facilitates a convenient semiclassical analysis of the Ponzano–Regge model, which yields as the dominant contribution to the amplitude the cosine of the Regge action in agreement with previous studies. We also consider the asymptotics of the SU(2) 6jsymbol using the noncommutative phase space path integral for the Ponzano–Regge model, and explain the connection of our results to the previous asymptotic results in terms of coherent states. Key words: Ponzano–Regge model; noncommutative representation; asymptotic analysis
Null twisted geometries
 Phys.Rev. D89 (2014) 084070 [1311.3279
"... We define and investigate a quantization of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrization of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantizatio ..."
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We define and investigate a quantization of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrization of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with spacelike faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalism are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, Abelian geometric picture. It can be described by a Euclidean singular structure on the twodimensional spacelike surface defined by a foliation of spacetime by null hypersurfaces. This geometric structure is naturally decomposed into a conformal metric and scale factors, forming locally conjugate pairs. Proper actionangle variables on the gaugeinvariant phase space are described by the eigenvectors of the Laplacian of the dual graph. We also identify the variables of the phase space amenable to characterize the extrinsic geometry of the foliation. Finally, we quantize the phase space and its algebra using Dirac’s algorithm, obtaining a notion of spin networks for null hypersurfaces. Such spin networks are labeled by SO(2) quantum numbers, and are embedded nontrivially in the unitary, infinitedimensional irreducible representations of the Lorentz group. 1