Area–angle variables for general relativity

By B. Dittrich, Simone Speziale. 2008

158 citations recorded by the source corpus.

We introduce a modified Regge calculus for general relativity on a triangulated four-dimensional Riemannian manifold where the fundamental variables are areas and a certain class of angles. These variables satisfy constraints which are local in the triangulation. We expect the formulation to have applications to classical discrete gravity and non-perturbative approaches to quantum gravity.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1745d9b5f7b4731c1a525d0203b42ebf6cbd9e75

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

The Spin-Foam Approach to Quantum Gravity (2012, background): “This question is quite an important one and has been one of the central concerns of the work led by Dittrich and collaborators for the last few years [151, 147, 150, 144, 43].”
Phase space descriptions for simplicial 4D geometries (2008, methodology): “which follow from the fact that the Gauß, simplicity, cross-simplicity and edge simplicity constraints allow us to conclude that the (dual) bivectors come from the edge vectors of tetrahedra, see also the discussion in [1].”
Twisted geometries: A geometric parametrisation of SU(2) phase space (2010, background): “To match the shapes one needs additional gluing constraints [27], which involve only the dihedral angles φee′ , and are local on each pair of tetrahedra.”
Asymptotic analysis of the EPRL four-simplex amplitude (2009, methodology): “(7) These intertwiners were introduced by Livine and Speziale [12], who gave an asymptotic formula for their normalisation.”
Improved and Perfect Actions in Discrete Gravity (2009, background): “However, in performing the continuum limit for both actions, we will demonstrate that they both converge to the same perfect action, when Λ and κ satisfy the relation (3.3).”
Twistors to twisted geometries (2010, background): “Finally, for graphs dual to triangulations, the space of closed twisted geometries can be related to the phase space of Regge calculus when one further imposes the gluing or shape matching conditions [10].”
The continuum limit of loop quantum gravity - a framework for solving the theory (2014, background): “rful and requires the continuum limit: For a system with such a symmetry it means that, given a solution, we can move the vertices around (i.e. change the 9 Alternatively one can use areas and angles [58], which is nearer to the variables used in spin foams. 10That is the Hessian of the action evalu”
Lorentzian spin foam amplitudes: graphical calculus and asymptotics (2009, unknown): “leaving the two further degrees of freedom of a tetrahedron geometry uncorrelated. This is somewhat similar to the geometry of a version of Regge calculus based only on areas, instead of lengths, cf. [18]. For γ<1 the two constructions of [6, 7] and [8, 9] are equivalent, meaning one has both a L”
Loop Quantum Gravity (2003, background): “5 Such areas and angles can be chosen as variables for describing the gravitational field [26].”
Asymptotic analysis of the Engle–Pereira–Rovelli–Livine four-simplex amplitude (2009, methodology): “(7) These intertwiners were introduced by Livine and Speziale [12], who gave an asymptotic formula for their normalisation.”
Polyhedra in loop quantum gravity (2010, background): “If both polyhedra are tetrahedra, the problem has been solved in [19].”
On the semiclassical limit of 4d spin foam models (2008, background): “Several studies have been launched in order to tackle this problem (see for instance [33, 34, 35]), but the results show that performing this explicitly is an incredibly difficult algebraic task.”