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Coarse graining methods for spin net and spin foam models
 HOLONOMY SPIN FOAM MODELS: DEFINITION AND COARSE GRAINING,” PHYS. REV. D 87, 044048 (2013) [ARXIV:1208.3388 [GRQC
, 2011
"... 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 19 (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
 SIGMA
, 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.
Group field theories for all loop quantum gravity
"... Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories ..."
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Cited by 3 (1 self)
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Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the gft formulation of the kkl spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes. 1
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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Cited by 3 (3 self)
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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
, 2013
"... 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 ..."
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Cited by 2 (0 self)
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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.