Discrete gravity as a local theory of the Poincaré group in the first-order formalism

Gionti, Gabriele

doi:10.1088/0264-9381/22/20/004

Cited by 10 publications

(13 citation statements)

References 22 publications

(85 reference statements)

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“…-On the other side, in the constrained case of gravity e provides the basis for the geometric 'simple' n-forms (and for the ω's conjugate momenta 2-forms, in this way). In the end, one could expect similarity of the discretization with the variant of Regge calculus that comes from the gauge theoretic approach to gravity [56,57]. The discrete e-field is likely to appear in the 'integrated' form (i.e.…”

Section: Discussionmentioning

confidence: 99%

Poincaré–Plebański formulation of GR and dual simplicity constraints

Belov

2018

Class. Quantum Grav.

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We revise the classical continuum formulation behind the Spin Foam approach to the quantization of gravity. Based on the recent applications of the current EPRL-FK model beyond triangulations, we identify the tension with the implementation of the 'volume' part of simplicity constraints, required for the passage from the topological BF theory to gravity. The crucial role, played by 4d normals in the linear version of constraints, necessitates the extension of the configuration space, and we argue to switch from normal 3-forms directly to tetrads. The requirement of vanishing torsion leads to consider first an unconstrained extended Poincaré BF theory, which we characterize fully both at the Lagrangian and Hamiltonian levels, paying special attention to its gauge symmetries. The simplicity constraints are introduced naturally, in the spirit of Plebański formulation, and we give their tetradic version, dual to that of using 3-forms. This brings us much closer to the geometric content of General Relativity.

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Section: Discussionmentioning

confidence: 99%

Poincaré–Plebański formulation of GR and dual simplicity constraints

Belov

2018

Class. Quantum Grav.

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“…and the PL spin connection ω ab µ (ǫ * ), where ǫ * is the dual edge connecting the centers of two adjacent 4-simplexes, see [16]. 6…”

Section: Vilenkin Wavefunctionmentioning

confidence: 99%

Piecewise Flat Metrics and Quantum Gravity

Mikovic

2020

Preprint

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We introduce a physical piecewise linear metric associated to a Regge triangulation of a smooth 4-manifold. We describe the basic properties of the corresponding geometry in the cases of the Euclidean and the Minkowski signature. In the Minkowski case, we describe the Regge action and how to define the corresponding path integral for the casual triangulations. We also discus the Regge path integral for a triangulation associated to the Friedman-Lemaitre-Robertson-Walker cosmological model and briefly study the corresponding wavefunctions, namely the Hartle-Hawking and the Vilenkin wavefunction.

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“…Interestingly enough, the closure constraint on the n − bein b, section 2; Eq. (13), implies that if we fix the link αβ and the corresponding b a αβ (α) and sum over all other n − beins originating from the dual vetrex α, we get…”

Section: Barrett-crane Quantizationmentioning

confidence: 99%

“…2 for all details) suggest the expansion of the exponential of the action in characters χ J U h of the irreducible representations J of the group SO(4), as in lattice Gauge Theory. We can omit the index αα in the holonomy matrix U h , since it does not depend on the starting simplex α,13 …”

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confidence: 99%