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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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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.
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
On the relations between gravity and BF theories
"... Abstract. We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both selfdual and nonchiral formulations, their generalizations, and the MacDowell– Mansouri action. ..."
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Abstract. We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both selfdual and nonchiral formulations, their generalizations, and the MacDowell– Mansouri action.
Quantum Cosmology from Group Field Theory Condensates: a Review
, 2016
"... Abstract. We give, in some detail, a critical overview over recent work towards deriving a cosmological phenomenology from the fundamental quantum dynamics of group field theory (GFT), based on the picture of a macroscopic universe as a "condensate" of a large number of quanta of geometry ..."
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Abstract. We give, in some detail, a critical overview over recent work towards deriving a cosmological phenomenology from the fundamental quantum dynamics of group field theory (GFT), based on the picture of a macroscopic universe as a "condensate" of a large number of quanta of geometry which are given by excitations of the GFT field over a "nospace" vacuum. We emphasise conceptual foundations, relations to other research programmes in GFT and the wider context of loop quantum gravity (LQG), and connections to the quantum physics of real BoseEinstein condensates. We show how to extract an effective dynamics for GFT condensates from the microscopic GFT physics, and how to compare it with predictions of more conventional quantum cosmology models, in particular loop quantum cosmology (LQC). No detailed familiarity with the GFT formalism is assumed.
Contents
, 2006
"... The proof planning systems available today are sequential systems. The hypothesis of this project is that the engineering of a proof planning system that is capable of dynamic, distributed, parallel proof planning will empower the paradigm of proof planning by unlocking its latent potential for thes ..."
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The proof planning systems available today are sequential systems. The hypothesis of this project is that the engineering of a proof planning system that is capable of dynamic, distributed, parallel proof planning will empower the paradigm of proof planning by unlocking its latent potential for these features. The system will be built on IsaPlanner, which is a proof planning system developed by Lucas Dixon (Dixon, 2005), based on the theorem prover, Isabelle. Alice, is an extension of Standard ML, with additional features for supporting concurrent, distributed programming. This is the choice for the implementation language for the purpose of this project. The methodology for the evaluation and the choice of test cases will also be outlined.